(D) The time of flight $T$ is given by $T = \sqrt{\frac{2h}{g}} = \sqrt{\frac{2 \times 5}{10}} = 1 \ s$.Let $v_b$ be the velocity of the ball and $v_u

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(D) The time of flight $T$ is given by $T = \sqrt{\frac{2h}{g}} = \sqrt{\frac{2 \times 5}{10}} = 1 \ s$.Let $v_b$ be the velocity of the ball and $v_u$ be the velocity of the bullet after the collision.For the ball: $20 = v_b \times T \implies v_b = 20 \ m/s$.For the bullet: $100 = v_u \times T \implies v_u = 100 \ m/s$.Applying the law of conservation of linear momentum in the horizontal direction:$m_{bullet} V = m_{ball} v_b + m_{bullet} v_u$$0.01 \times V = 0.2 \times 20 + 0.01 \times 100$$0.01 V = 4 + 1$$0.01 V = 5$$V = 500 \ m/s$.

Class 11 Physics Work, Energy, Power and Collision Mix Examples-Work, Energy, Power and Collision

Difficult

$A$ ball of mass $0.2 \ kg$ is at rest at a height of $5 \ m$. $A$ bullet of mass $0.01 \ kg$ moving horizontally with a velocity $V \ m/s$ strikes the center of the ball. After the collision,the ball and the bullet move independently. The ball hits the ground at a distance of $20 \ m$ and the bullet hits the ground at a distance of $100 \ m$ from the base of the pillar. What is the initial velocity $V$ of the bullet in $m/s$?

A
$250$
B
$250 \sqrt{2}$
C
$400$
D
$500$

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Work, Energy, Power and Collision

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Mix Examples-Work, Energy, Power and Collision

$A$ small ball of mass $m$ starts at a point $A$ with speed $v_0$ and moves along a frictionless track $AB$ as shown. The track $BC$ has a coefficient of friction $\mu$. The ball comes to a stop at $C$ after traveling a distance $L$. The value of $L$ is:

DifficultJEE MAIN 2014

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Two identical blocks $A$ and $B$,each of mass $m$,resting on a smooth horizontal floor,are connected by a light spring of natural length $L$ and spring constant $K$. $A$ third block $C$ of mass $m$,moving with a speed $v$ along the line joining $A$ and $B$,collides with $A$. The maximum compression in the spring is:

DifficultJEE MAIN 2021

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$A$ $1.0\, kg$ block collides with a horizontal weightless spring of force constant $2.75\, N/m$ as shown in the figure. The block compresses the spring $4.0\, m$ from the rest position. If the coefficient of kinetic friction between the block and the horizontal surface is $0.25$,the speed of the block at the instant of collision is ................. $m/s$.

Medium

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$A$ particle of mass $m$ is projected from the ground with an initial speed $u_0$ at an angle $\alpha$ with the horizontal. At the highest point of its trajectory,it makes a completely inelastic collision with another identical particle,which was thrown vertically upward from the ground with the same initial speed $u_0$. The angle that the composite system makes with the horizontal immediately after the collision is :

DifficultIIT 2013

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In the case of circular motion of a body,if a tangential force also acts on the body in addition to a centripetal force,then the work done:

Medium

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$A$ small ball of mass $m$ starts at a point $A$ with speed $v_0$ and moves along a frictionless track $AB$ as shown. The track $BC$ has a coefficient of friction $\mu$. The ball comes to a stop at $C$ after traveling a distance $L$. The value of $L$ is:

In the case of circular motion of a body,if a tangential force also acts on the body in addition to a centripetal force,then the work done:

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