A spherical rigid ball is released from rest and starts rolling d… - Vidyadip

MCQ

A spherical rigid ball is released from rest and starts rolling down an inclined plane from height $h=7 \,m$, as shown in the figure. It hits a block at rest on the horizontal plane (assume elastic collision). If the mass of both the ball and the block is $m$ and the ball is rolling without sliding, then the speed of the block after collision is close to ............. $m/s$

A
$6$
B
$8$
✓
$10$
D
$12$

✓

Answer

Correct option: C.

$10$

c
$(c)$ As collision is elastic and masses of colliding objects are equal, so there is exchange of total energy of moving mass to stationary mass.

Hence, velocity of block = velocity of sphere just before collision.

For sphere, if $v=$ velocity of translation of centre of mass at the bottom of plane and $\omega=$ angular speed, then by energy conservation, we have

$m g h=\frac{1}{2} m v^{2}+\frac{1}{2} I \omega^{2}$

Here, $\omega=\frac{v}{R}$ and $\quad I=\frac{2}{5} m R^{2}$

Substituting and solving for velocity, we have

$v=\sqrt{\frac{10}{7} g h}=\sqrt{\frac{10 \times 10 \times 7}{7}}=10 \,m / s$

$\therefore$ Velocity of block after collision $=10 \,m / s$

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