(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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Vertical Circular Motion

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$A$ point mass '$m$' is moved in a vertical circle of radius '$r$' with the help of a string. The velocity of the mass is $\sqrt{7gr}$ at the lowest point. The tension in the string at the lowest point is .......... $mg$.

MediumNEET 2020

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$A$ particle is tied to a $20 \ cm$ long string. It performs circular motion in a vertical plane. What is the angular speed of the particle when the tension in the string at the top is zero? (Take $g = 9.8 \ m/s^2$)

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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

$A$ weightless thread can bear tension up to $3.7 \ kg \ wt$. $A$ stone of mass $500 \ g$ is tied to it and revolved in a circular path of radius $4 \ m$ in a vertical plane. The maximum angular velocity of the stone will be (acceleration due to gravity,$g = 10 \ m/s^2$) (in $rad/s$)

$A$ particle is rotated in a vertical circle by connecting it to a light rod of length $l$ and keeping the other end of the rod fixed. The minimum speed of the particle when the light rod is horizontal for which the particle will complete the circle is

$A$ bucket tied at the end of a $1.6\, m$ long string is whirled in a vertical circle with constant speed. What should be the minimum speed so that the water from the bucket does not spill,when the bucket is at the highest position? (Take $g = 10\, m/s^2$)

$A$ point mass '$m$' is moved in a vertical circle of radius '$r$' with the help of a string. The velocity of the mass is $\sqrt{7gr}$ at the lowest point. The tension in the string at the lowest point is .......... $mg$.

$A$ particle is tied to a $20 \ cm$ long string. It performs circular motion in a vertical plane. What is the angular speed of the particle when the tension in the string at the top is zero? (Take $g = 9.8 \ m/s^2$)

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