(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

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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

The minimum velocity $v$ required for a simple pendulum to complete one full rotation in a vertical plane is given. If the length of the string is reduced to one-fourth,what will be the new required velocity?

$A$ body of mass $m$ is tied to a string of length $l$ and rotated in a vertical circle. What is the difference in tension between the lowest point and the highest point (in $,mg$)?

$ABCDE$ is a channel in the vertical plane,part $BCDE$ being circular with radius $r$. $A$ block is released from $A$ and slides without friction and without rolling. The block will complete the loop if $h$ is

$A$ bucket filled with water is revolved in a vertical circle of radius $4 \ m$ and the water just does not fall down. The time period of revolution will be ........ $s$.

The string of a pendulum of length $l$ is displaced through $90^{\circ}$ from the vertical and released. The minimum strength of the string required to withstand the tension as the pendulum passes through the mean position is:

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