(D) By the law of conservation of linear momentum during the collision:$mv = M V' + m(v/2)$$mv - mv/2 = M V'$$mv/2 = M V'$$V' = \frac{mv}{2M}$For the

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

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

Difficult

$A$ bullet of mass $m$ and velocity $v$ strikes the bob of a pendulum of mass $M$ and emerges out with velocity $v/2$. What is the minimum value of $v$ such that the bob of the pendulum will swing through a complete circle? (Take the length of the pendulum $= \ell$)

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

$A$ heavy mass is attached to a thin wire and is whirled in a vertical circle. The wire is most likely to break:

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$A$ bucket filled with water is tied to a rope of length $0.5 \,m$ and is rotated in a circular path in a vertical plane. The minimum velocity it should have at the lowest point of the circle so that the water does not spill is, $(g=10 \,m/s^2)$

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What is the minimum velocity at the lowest point of a vertical circle of radius $l$ such that the string just becomes slack at the highest point?

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$A$ block of mass $m$ is given a velocity $20\ m/s$ on a horizontal rough surface of length $x\ m$. After the rough surface,there is a vertical circular path of radius $R = 2\ m$ which is frictionless. The block enters the circular path with the minimum velocity required to complete the path. Find the length of the rough surface $x$ if the coefficient of friction is $\mu = 0.5$.

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$A$ stone of mass $1 \ kg$ tied to a light inextensible string of length $L = \frac{5}{3} \ m$ is rotating in a circular path of radius $L$ in a vertical plane. If the ratio of maximum tension in the string to the minimum tension in the string is $3$,the speed of the stone at the highest point of the circle is ($g =$ acceleration due to gravity).

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$A$ bullet of mass $m$ and velocity $v$ strikes the bob of a pendulum of mass $M$ and emerges out with velocity $v/2$. What is the minimum value of $v$ such that the bob of the pendulum will swing through a complete circle? (Take the length of the pendulum $= \ell$)

Similar Questions

$A$ heavy mass is attached to a thin wire and is whirled in a vertical circle. The wire is most likely to break:

$A$ bucket filled with water is tied to a rope of length $0.5 \,m$ and is rotated in a circular path in a vertical plane. The minimum velocity it should have at the lowest point of the circle so that the water does not spill is, $(g=10 \,m/s^2)$

What is the minimum velocity at the lowest point of a vertical circle of radius $l$ such that the string just becomes slack at the highest point?

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