(D) By the principle of conservation of linear momentum during the collision:$m v = m(v/2) + M v_1$,where $v_1$ is the velocity acquired by the pendul

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(D) By the principle of conservation of linear momentum during the collision:$m v = m(v/2) + M v_1$,where $v_1$ is the velocity acquired by the pendulum bob.$M v_1 = m(v - v/2) = mv/2$$v_1 = \frac{m}{2M} v$For the pendulum bob to complete a full vertical circle,the minimum velocity at the lowest point must be $v_1 = \sqrt{5g\ell}$.Equating the two expressions for $v_1$:$\frac{m}{2M} v = \sqrt{5g\ell}$$v = \frac{2M}{m} \sqrt{5g\ell}$

Class 11 Physics Work, Energy, Power and Collision Vertical Circular Motion

Medium

$A$ bullet of mass $m$ moving with velocity $v$ passes through a pendulum bob of mass $M$ and emerges with a velocity $v/2$. What is the minimum value of $v$ so that the pendulum bob completes a full vertical circle of length $\ell$?

A
$\frac{M}{m} \sqrt{2\ell g}$
B
$\frac{2M}{m} \sqrt{2\ell g}$
C
$\frac{M}{2m} \sqrt{5\ell g}$
D
$\frac{2M}{m} \sqrt{5\ell g}$

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Work, Energy, Power and Collision

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Vertical Circular Motion

$A$ particle of mass $m$ is tied to a string of length $l$ and whirled in a vertical circle. The difference in tension and kinetic energy at the highest and lowest positions of the circular path will be:

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As per the given figure,to complete the circular loop,what should be the radius if the initial height is $5 \, m$ (in $, m$)?

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$A$ block of mass $m$ at the end of a string is whirled round in a vertical circle of radius $R$. The critical speed of the block at the top of its swing below which the string would slacken before the block reaches the top is

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$A$ particle of mass $200 \,g$ is whirled in a vertical circle of radius $80 \,cm$ using a massless string. The speed of the particle when the string makes an angle of $60^{\circ}$ with the vertical line is $1.5 \,m/s$. The tension in the string at this position is ........... $N$.

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$A$ bucket filled with water is tied to a string of length $4 \ m$ and rotated in a vertical circle. To ensure that the water does not spill,the time period of rotation should be ........ $s$.

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$A$ bullet of mass $m$ moving with velocity $v$ passes through a pendulum bob of mass $M$ and emerges with a velocity $v/2$. What is the minimum value of $v$ so that the pendulum bob completes a full vertical circle of length $\ell$?

Similar Questions

$A$ particle of mass $m$ is tied to a string of length $l$ and whirled in a vertical circle. The difference in tension and kinetic energy at the highest and lowest positions of the circular path will be:

As per the given figure,to complete the circular loop,what should be the radius if the initial height is $5 \, m$ (in $, m$)?

$A$ block of mass $m$ at the end of a string is whirled round in a vertical circle of radius $R$. The critical speed of the block at the top of its swing below which the string would slacken before the block reaches the top is

$A$ particle of mass $200 \,g$ is whirled in a vertical circle of radius $80 \,cm$ using a massless string. The speed of the particle when the string makes an angle of $60^{\circ}$ with the vertical line is $1.5 \,m/s$. The tension in the string at this position is ........... $N$.

$A$ bucket filled with water is tied to a string of length $4 \ m$ and rotated in a vertical circle. To ensure that the water does not spill,the time period of rotation should be ........ $s$.

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