NEET Physics Motion of System of Particles and Rigid Body NEET s MCQ Questions - Practice Now

Question 1

The angular speed of a flywheel moving with uniform angular acceleration changes from $\text{1200 rpm}$ to $\text{3120 rpm}$ in $\text{16 seconds}$. The angular acceleration (in $\mathrm{rad\ s^{-2}}$)is

Accepted Answer

<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>4</mn><mi>π</mi></mrow><annotation encoding="application/x-tex">4\pi</annotation></semantics></math>4π

Answer

<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2</mn><mi>π</mi></mrow><annotation encoding="application/x-tex">2\pi</annotation></semantics></math>2π

Answer

<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>12</mn><mi>π</mi></mrow><annotation encoding="application/x-tex">12\pi</annotation></semantics></math>12π

Answer

<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>104</mn><mi>π</mi></mrow><annotation encoding="application/x-tex">104\pi</annotation></semantics></math>104π

Question 2

Two objects of mass $10 \mathrm{kg}$ and $20 \mathrm{kg}$ respectively are connected to the two ends of a rigid rod of length $10 \mathrm{m}$ with negligible mass. The distance of the centre of mass of the system from the $10 \mathrm{kg}$ mass is

Accepted Answer

<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>20</mn><mn>3</mn></mfrac></mstyle><mi mathvariant="normal">m</mi></mrow><annotation encoding="application/x-tex">\dfrac {20}{3}\mathrm m</annotation></semantics></math>320​m

Answer

<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>10</mn><mn>3</mn></mfrac></mstyle><mi mathvariant="normal">m</mi></mrow><annotation encoding="application/x-tex">\dfrac {10}{3}\mathrm m</annotation></semantics></math>310​m

Answer

<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>10</mn><mi mathvariant="normal">m</mi></mrow><annotation encoding="application/x-tex">10\mathrm m</annotation></semantics></math>10m

Answer

<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>5</mn><mi mathvariant="normal">m</mi></mrow><annotation encoding="application/x-tex">5\mathrm m</annotation></semantics></math>5m

Question 3

The ratio of the radius of gyration of a thin uniform disc about an axis passing through its centre and normal to its plane to the radius of gyration of the disc about its diameter is:

Accepted Answer

<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msqrt><mn>2</mn></msqrt><mo>:</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">\sqrt 2:1</annotation></semantics></math>2<svg width="400em" height="1.08em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
c69,-144,104.5,-217.7,106.5,-221
l0 -0
c5.3,-9.3,12,-14,20,-14
H400000v40H845.2724
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z"></path></svg>​:1

Answer

<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2</mn><mo>:</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">2:1</annotation></semantics></math>2:1

Answer

<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>4</mn><mo>:</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">4:1</annotation></semantics></math>4:1

Answer

<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn><mo>:</mo><msqrt><mn>2</mn></msqrt></mrow><annotation encoding="application/x-tex">1:\sqrt 2</annotation></semantics></math>1:2<svg width="400em" height="1.08em" viewBox="0 0 400000 1080" preserveAspectRatio="xMinYMin slice"><path d="M95,702
c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14
c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429
c69,-144,104.5,-217.7,106.5,-221
l0 -0
c5.3,-9.3,12,-14,20,-14
H400000v40H845.2724
s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7
c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z
M834 80h400000v40h-400000z"></path></svg>​

Question 4

A uniform rod of length $200\ \text{cm}$ and mass $500\ \text{g}$ is balanced on a wedge placed at $40\ \text{cm}$ mark. A mass of $2\ \text{kg}$ is suspended from the rod at $20\ \text{cm}$ and another unknown mass $m$ is suspended from the rod at $160\ \text{cm}$ mark as shown in the figure. Find the value of $m$ such that the rod is in equilibrium. (${g=10\ \mathrm{m/s^2}}$)

Accepted Answer

<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>1</mn><mn>12</mn></mfrac></mstyle><mtext> kg </mtext></mrow><annotation encoding="application/x-tex">{\dfrac{1}{12}\ 	ext{kg }}</annotation></semantics></math>121​ kg

Answer

<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>1</mn><mn>3</mn></mfrac></mstyle><mtext> kg </mtext></mrow><annotation encoding="application/x-tex">{\dfrac{1}{3}\ 	ext{kg }}</annotation></semantics></math>31​ kg

Answer

<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>1</mn><mn>6</mn></mfrac></mstyle><mtext> kg </mtext></mrow><annotation encoding="application/x-tex">{\dfrac{1}{6} \ 	ext{kg }}</annotation></semantics></math>61​ kg

Answer

<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>1</mn><mn>2</mn></mfrac></mstyle><mtext> kg </mtext></mrow><annotation encoding="application/x-tex">{\dfrac{1}{2}\ 	ext{kg }}</annotation></semantics></math>21​ kg

Question 5

A horizontal platform is rotating with a uniform angular velocity around the vertical axis passing through its centre. At some instant, viscous fluid of mass $m$ is dropped at the centre and is allowed to spread out and finally fall. The angular velocity during this period

Accepted Answer

Decreases initially and increases again

Answer

Decreases continuously

Answer

Remains unaltered

Answer

Increases continuously

Question 6

A thin circular ring of mass $M$ and radius $R$ is rotating in a horizontal plane about an axis vertical to its plane with a constant angular velocity $\omega$, If two objects each mass $m$ be attached gently to the opposite ends of a diameter of the ring, the ring, will then rotate with an angular velocity

Accepted Answer

<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mstyle displaystyle="true" scriptlevel="0"><mfrac><mrow><mi>M</mi><mi>ω</mi></mrow><mrow><mi>M</mi><mo>+</mo><mn>2</mn><mi>m</mi></mrow></mfrac></mstyle></mrow><annotation encoding="application/x-tex">\dfrac{M\omega}{M+2m}</annotation></semantics></math>M+2mMω​

Answer

<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mstyle displaystyle="true" scriptlevel="0"><mfrac><mrow><mo stretchy="false">(</mo><mi>M</mi><mo>+</mo><mn>2</mn><mi>m</mi><mo stretchy="false">)</mo><mi>ω</mi></mrow><mrow><mn>2</mn><mi>m</mi></mrow></mfrac></mstyle></mrow><annotation encoding="application/x-tex">\dfrac{(M+2m)\omega}{2m}</annotation></semantics></math>2m(M+2m)ω​

Answer

<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mstyle displaystyle="true" scriptlevel="0"><mfrac><mrow><mn>2</mn><mi>M</mi><mi>ω</mi></mrow><mrow><mi>M</mi><mo>+</mo><mn>2</mn><mi>m</mi></mrow></mfrac></mstyle></mrow><annotation encoding="application/x-tex">\dfrac{2M\omega}{M+2m}</annotation></semantics></math>M+2m2Mω​

Answer

<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mstyle displaystyle="true" scriptlevel="0"><mfrac><mrow><mo stretchy="false">(</mo><mi>M</mi><mo>+</mo><mn>2</mn><mi>m</mi><mo stretchy="false">)</mo><mi>ω</mi></mrow><mi>M</mi></mfrac></mstyle></mrow><annotation encoding="application/x-tex">\dfrac{(M+2m)\omega}{M}</annotation></semantics></math>M(M+2m)ω​

Question 7

A man of $50\mathrm{\ kg}$ mass is standing in a gravity free space at a height of $10\mathrm{\ m}$ above the floor. He throws a stone of $0.5\mathrm{\ kg}$ mass downwards with a speed $2\mathrm{\ m\ s^{-1}}$. When the stone reaches the floor, the distance of the man above the floor will be

Accepted Answer

<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>10.1</mn><mrow><mtext> </mtext><mi mathvariant="normal">m</mi></mrow></mrow><annotation encoding="application/x-tex">10.1\mathrm{\ m}</annotation></semantics></math>10.1 m

Answer

<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>20</mn><mrow><mtext> </mtext><mi mathvariant="normal">m</mi></mrow></mrow><annotation encoding="application/x-tex">20\mathrm{\ m}</annotation></semantics></math>20 m

Answer

<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>9.9</mn><mrow><mtext> </mtext><mi mathvariant="normal">m</mi></mrow></mrow><annotation encoding="application/x-tex">9.9\mathrm{\ m}</annotation></semantics></math>9.9 m

Answer

<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>10</mn><mrow><mtext> </mtext><mi mathvariant="normal">m</mi></mrow></mrow><annotation encoding="application/x-tex">10\mathrm{\ m}</annotation></semantics></math>10 m

Question 8

ABC is an equilateral triangle with O as its center. ${\vec{F}_1}$, ${\vec{F}_2}$, and ${\vec{F}_3}$ represent three forces acting along teh sides AB, BC, and AC, respectively. If the total torque about O is zero then the magnitude of ${\vec{F}_3}$ is

Accepted Answer

<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mover accent="true"><mi>F</mi><mo>⃗</mo></mover><mn>1</mn></msub><mo>+</mo><msub><mover accent="true"><mi>F</mi><mo>⃗</mo></mover><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">{\vec{F}_1+\vec{F}_2}</annotation></semantics></math>F<svg width="0.471em" height="0.714em" style="width:0.471em" viewBox="0 0 471 714" preserveAspectRatio="xMinYMin"><path d="M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5
3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11
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-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1
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c-16-25.333-24-45-24-59z"></path></svg>1​+F<svg width="0.471em" height="0.714em" style="width:0.471em" viewBox="0 0 471 714" preserveAspectRatio="xMinYMin"><path d="M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5
3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11
10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63
-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1
-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59
H213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359
c-16-25.333-24-45-24-59z"></path></svg>2​

Answer

<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mstyle displaystyle="true" scriptlevel="0"><mfrac><mrow><msub><mover accent="true"><mi>F</mi><mo>⃗</mo></mover><mn>1</mn></msub><mo>+</mo><msub><mover accent="true"><mi>F</mi><mo>⃗</mo></mover><mn>2</mn></msub></mrow><mn>2</mn></mfrac></mstyle></mrow><annotation encoding="application/x-tex">{\dfrac{\vec{F}_1+\vec{F}_2}{2}}</annotation></semantics></math>2F<svg width="0.471em" height="0.714em" style="width:0.471em" viewBox="0 0 471 714" preserveAspectRatio="xMinYMin"><path d="M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5
3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11
10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63
-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1
-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59
H213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359
c-16-25.333-24-45-24-59z"></path></svg>1​+F<svg width="0.471em" height="0.714em" style="width:0.471em" viewBox="0 0 471 714" preserveAspectRatio="xMinYMin"><path d="M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5
3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11
10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63
-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1
-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59
H213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359
c-16-25.333-24-45-24-59z"></path></svg>2​​

Answer

<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2</mn><mo stretchy="false">(</mo><msub><mover accent="true"><mi>F</mi><mo>⃗</mo></mover><mn>1</mn></msub><mo>+</mo><msub><mover accent="true"><mi>F</mi><mo>⃗</mo></mover><mn>2</mn></msub><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">2(\vec{F}_1+\vec{F}_2)</annotation></semantics></math>2(F<svg width="0.471em" height="0.714em" style="width:0.471em" viewBox="0 0 471 714" preserveAspectRatio="xMinYMin"><path d="M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5
3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11
10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63
-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1
-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59
H213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359
c-16-25.333-24-45-24-59z"></path></svg>1​+F<svg width="0.471em" height="0.714em" style="width:0.471em" viewBox="0 0 471 714" preserveAspectRatio="xMinYMin"><path d="M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5
3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11
10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63
-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1
-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59
H213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359
c-16-25.333-24-45-24-59z"></path></svg>2​)

Answer

<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mover accent="true"><mi>F</mi><mo>⃗</mo></mover><mn>1</mn></msub><mo>−</mo><msub><mover accent="true"><mi>F</mi><mo>⃗</mo></mover><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">{\vec{F}_1-\vec{F}_2}</annotation></semantics></math>F<svg width="0.471em" height="0.714em" style="width:0.471em" viewBox="0 0 471 714" preserveAspectRatio="xMinYMin"><path d="M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5
3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11
10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63
-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1
-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59
H213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359
c-16-25.333-24-45-24-59z"></path></svg>1​−F<svg width="0.471em" height="0.714em" style="width:0.471em" viewBox="0 0 471 714" preserveAspectRatio="xMinYMin"><path d="M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5
3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11
10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63
-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1
-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59
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c-16-25.333-24-45-24-59z"></path></svg>2​

Question 9

The moment of the force at $(2,0,-3)$, about the point $(2,-2,-2)$ is given by __.

Where, $F=4i+5i-6k\ $

Accepted Answer

<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo><mn>7</mn><mover accent="true"><mi>i</mi><mo>^</mo></mover><mo>−</mo><mn>4</mn><mover accent="true"><mi>j</mi><mo>^</mo></mover><mo>−</mo><mn>8</mn><mover accent="true"><mi>k</mi><mo>^</mo></mover></mrow><annotation encoding="application/x-tex">-7\hat{i}-4\hat{j}-8\hat{k}</annotation></semantics></math>−7i^−4j^​−8k^

Answer

<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo><mn>8</mn><mover accent="true"><mi>i</mi><mo>^</mo></mover><mo>−</mo><mn>4</mn><mover accent="true"><mi>j</mi><mo>^</mo></mover><mo>−</mo><mn>7</mn><mover accent="true"><mi>k</mi><mo>^</mo></mover></mrow><annotation encoding="application/x-tex">-8\hat{i}-4\hat{j}-7\hat{k}</annotation></semantics></math>−8i^−4j^​−7k^

Answer

<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo><mn>4</mn><mover accent="true"><mi>i</mi><mo>^</mo></mover><mo>−</mo><mover accent="true"><mi>j</mi><mo>^</mo></mover><mo>−</mo><mn>8</mn><mover accent="true"><mi>k</mi><mo>^</mo></mover></mrow><annotation encoding="application/x-tex">-4\hat{i}-\hat{j}-8\hat{k}</annotation></semantics></math>−4i^−j^​−8k^

Answer

<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo><mn>7</mn><mover accent="true"><mi>i</mi><mo>^</mo></mover><mo>−</mo><mn>8</mn><mover accent="true"><mi>j</mi><mo>^</mo></mover><mo>−</mo><mn>4</mn><mover accent="true"><mi>k</mi><mo>^</mo></mover></mrow><annotation encoding="application/x-tex">-7\hat{i}-8\hat{j}-4\hat{k}</annotation></semantics></math>−7i^−8j^​−4k^

Question 10

A solid cylinder of mass m and radius $R$ rolls down an inclined plane of height $h$ without slipping. The speed of its centre of mass when it reaches the bottom is

Accepted Answer

<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msqrt><mstyle displaystyle="true" scriptlevel="0"><mfrac><mrow><mn>4</mn><mi>g</mi><mi>h</mi></mrow><mn>3</mn></mfrac></mstyle></msqrt></mrow><annotation encoding="application/x-tex">\sqrt{\dfrac{4gh}{3}}</annotation></semantics></math>34gh​<svg width="400em" height="2.48em" viewBox="0 0 400000 2592" preserveAspectRatio="xMinYMin slice"><path d="M424,2478
c-1.3,-0.7,-38.5,-172,-111.5,-514c-73,-342,-109.8,-513.3,-110.5,-514
c0,-2,-10.7,14.3,-32,49c-4.7,7.3,-9.8,15.7,-15.5,25c-5.7,9.3,-9.8,16,-12.5,20
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s209,968,209,968c0,-2,84.7,-361.7,254,-1079c169.3,-717.3,254.7,-1077.7,256,-1081
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v40H1014.6
s-87.3,378.7,-272.6,1166c-185.3,787.3,-279.3,1182.3,-282,1185
c-2,6,-10,9,-24,9
c-8,0,-12,-0.7,-12,-2z M1001 80
h400000v40h-400000z"></path></svg>​

Answer

<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msqrt><mrow><mo stretchy="false">(</mo><mn>2</mn><mi>g</mi><mi>h</mi><mo stretchy="false">)</mo></mrow></msqrt></mrow><annotation encoding="application/x-tex">\sqrt{(2gh)}</annotation></semantics></math>(2gh)<svg width="400em" height="1.28em" viewBox="0 0 400000 1296" preserveAspectRatio="xMinYMin slice"><path d="M263,681c0.7,0,18,39.7,52,119
c34,79.3,68.167,158.7,102.5,238c34.3,79.3,51.8,119.3,52.5,120
c340,-704.7,510.7,-1060.3,512,-1067
l0 -0
c4.7,-7.3,11,-11,19,-11
H40000v40H1012.3
s-271.3,567,-271.3,567c-38.7,80.7,-84,175,-136,283c-52,108,-89.167,185.3,-111.5,232
c-22.3,46.7,-33.8,70.3,-34.5,71c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1
s-109,-253,-109,-253c-72.7,-168,-109.3,-252,-110,-252c-10.7,8,-22,16.7,-34,26
c-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26s76,-59,76,-59s76,-60,76,-60z
M1001 80h400000v40h-400000z"></path></svg>​

Answer

<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext>​​</mtext><msqrt><mstyle displaystyle="true" scriptlevel="0"><mfrac><mrow><mn>3</mn><mi>g</mi><mi>h</mi></mrow><mn>4</mn></mfrac></mstyle></msqrt></mrow><annotation encoding="application/x-tex">​​\sqrt{\dfrac{3gh}{4}}</annotation></semantics></math>​​43gh​<svg width="400em" height="2.48em" viewBox="0 0 400000 2592" preserveAspectRatio="xMinYMin slice"><path d="M424,2478
c-1.3,-0.7,-38.5,-172,-111.5,-514c-73,-342,-109.8,-513.3,-110.5,-514
c0,-2,-10.7,14.3,-32,49c-4.7,7.3,-9.8,15.7,-15.5,25c-5.7,9.3,-9.8,16,-12.5,20
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s209,968,209,968c0,-2,84.7,-361.7,254,-1079c169.3,-717.3,254.7,-1077.7,256,-1081
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v40H1014.6
s-87.3,378.7,-272.6,1166c-185.3,787.3,-279.3,1182.3,-282,1185
c-2,6,-10,9,-24,9
c-8,0,-12,-0.7,-12,-2z M1001 80
h400000v40h-400000z"></path></svg>​

Answer

<math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msqrt><mstyle displaystyle="true" scriptlevel="0"><mfrac><mrow><mn>4</mn><mi>g</mi></mrow><mi>h</mi></mfrac></mstyle></msqrt></mrow><annotation encoding="application/x-tex">\sqrt{\dfrac{4g}{h}}</annotation></semantics></math>h4g​<svg width="400em" height="2.48em" viewBox="0 0 400000 2592" preserveAspectRatio="xMinYMin slice"><path d="M424,2478
c-1.3,-0.7,-38.5,-172,-111.5,-514c-73,-342,-109.8,-513.3,-110.5,-514
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s209,968,209,968c0,-2,84.7,-361.7,254,-1079c169.3,-717.3,254.7,-1077.7,256,-1081
l0 -0c4,-6.7,10,-10,18,-10 H400000
v40H1014.6
s-87.3,378.7,-272.6,1166c-185.3,787.3,-279.3,1182.3,-282,1185
c-2,6,-10,9,-24,9
c-8,0,-12,-0.7,-12,-2z M1001 80
h400000v40h-400000z"></path></svg>​

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