(B) The velocity of each mass just before impact is $v_0 = \sqrt{2gh}$.After the collision,the velocities of the two masses are $v_1 = e_1 v_0$ and $v

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(B) The velocity of each mass just before impact is $v_0 = \sqrt{2gh}$.After the collision,the velocities of the two masses are $v_1 = e_1 v_0$ and $v_2 = e_2 v_0$ in the upward direction.The velocity of the centre of mass $(v_{cm})$ immediately after the collision is given by the average of the individual velocities:$v_{cm} = \frac{v_1 + v_2}{2} = \frac{e_1 \sqrt{2gh} + e_2 \sqrt{2gh}}{2} = \frac{(e_1 + e_2) \sqrt{2gh}}{2}$.Using the kinematic equation $v^2 = u^2 + 2as$,where $v=0$ at maximum height $h'$,$u = v_{cm}$,and $a = -g$:$0 = \left( \frac{(e_1 + e_2) \sqrt{2gh}}{2} \right)^2 - 2gh'$$2gh' = \frac{(e_1 + e_2)^2 (2gh)}{4}$$h' = \frac{(e_1 + e_2)^2 h}{4}$.

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

Difficult

$A$ dumbbell consisting of two masses $m$ each,connected by a light rigid rod of length $l$,falls from a height $h$ onto two pads of equal height,one steel and the other brass. The coefficients of restitution are $e_1$ and $e_2$ $(e_1 < e_2)$. To what maximum height will the centre of mass of the dumbbell rise after bouncing off the pads?

A
$\frac{h}{e_1 + e_2}$
B
$(e_1 + e_2)^2 \frac{h}{4}$
C
$\frac{e_1^2 + e_2^2}{4} \times h$
D
$\frac{4h}{e_1^2 + e_2^2}$

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Class 11 Questions

Class 11

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Work, Energy, Power and Collision

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Mix Examples-Work, Energy, Power and Collision

Assertion $(A)$: In an elastic collision of two billiard balls,the total kinetic energy $(KE)$ is conserved during the short time of collision of the balls (i.e.,when they are in contact).
Reason $(R)$: Energy spent against friction does not follow the law of conservation of energy.

MediumAP EAMCET 2021

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State whether the following statements are true or false:
$(a)$ Power is the vector product of force and velocity.
$(b)$ $1\,kg\,m = 9.8\,J$
$(c)$ When a teacher rubs a blackboard with a duster,they do no work.
$(d)$ Kinetic energy can be negative.

Medium

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$A$ and $B$ are blocks of same mass $m$ exactly equivalent to each other. Both are placed on a frictionless surface connected by a spring. The natural length of the spring is $L$ and the force constant is $K$. Initially,the spring is at its natural length. Another equivalent block $C$ of mass $m$ travelling at speed $v$ along the line joining $A$ and $B$ collides with $A$. In an ideal condition,the maximum compression of the spring is:

Difficult

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$A$ block of mass $m$ moving with a velocity $v_0$ on a smooth horizontal surface strikes and compresses a spring of stiffness $k$ until the mass comes to rest,as shown in the figure. This phenomenon is observed by two observers:
$A$: standing on the horizontal surface
$B$: standing on the block
According to observer $B$,the potential energy of the spring increases:

Medium

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$A$ $70\, kg$ man leaps vertically into the air from a crouching position. To take the leap,the man pushes the ground with a constant force $F$ to raise himself. The center of gravity rises by $0.5\, m$ before he leaves the ground. After the leap,the center of gravity rises by another $1\, m$. The maximum power delivered by the muscles is: (Take $g = 10\, ms^{-2}$)

DifficultJEE MAIN 2013

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Assertion $(A)$: In an elastic collision of two billiard balls,the total kinetic energy $(KE)$ is conserved during the short time of collision of the balls (i.e.,when they are in contact).Reason $(R)$: Energy spent against friction does not follow the law of conservation of energy.

State whether the following statements are true or false:$(a)$ Power is the vector product of force and velocity.$(b)$ $1\,kg\,m = 9.8\,J$$(c)$ When a teacher rubs a blackboard with a duster,they do no work.$(d)$ Kinetic energy can be negative.

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Assertion $(A)$: In an elastic collision of two billiard balls,the total kinetic energy $(KE)$ is conserved during the short time of collision of the balls (i.e.,when they are in contact).
Reason $(R)$: Energy spent against friction does not follow the law of conservation of energy.

State whether the following statements are true or false:
$(a)$ Power is the vector product of force and velocity.
$(b)$ $1\,kg\,m = 9.8\,J$
$(c)$ When a teacher rubs a blackboard with a duster,they do no work.
$(d)$ Kinetic energy can be negative.