Question

The figure shows a block having a small basket in it and an small inclined plane (with fixed angle) is rigidly attached to the block. The combined mass (including incline plane) of all these is M = 5 kg. Initially they are at rest. Now identical balls each of mass m=1 kg are thrown horizontally with velocity v = 5m/s (with respect to ground) which strike the inclined plane and then are collected in the small basket. Assume that in the basket balls come to rest with respect to basket. Choose the correct statement(s) from the following :

• A. After collecting 5 balls the speed of the block will be 2.5 m/s
• B. After collecting 10 balls the speed of the block will be (10/3) m/s
• C. The velocity of the block will never be exactly 5 m/s no matter how many balls are collected in the basket.
• D. Increase in speed of the block will be same every time for collection of each ball in the basket

Answer 1

Answer: (A), (B), (C)

The correct options are
A After collecting 5 balls the speed of the block will be 2.5 m/s
B After collecting 10 balls the speed of the block will be (10/3) m/s
C The velocity of the block will never be exactly 5 m/s no matter how many balls are collected in the basket.

Total momentum of $N$ balls
$=Nmv=N(1\times 5)=5N$
$\therefore$ Momentum of the block along with $N$ balls$=5N$ or
$(M+Nm)$ $v^{\prime }=5N$ where $v^{\prime }$ is the velocity of the block
After $N$ balls are collected in the basket.

$\therefore v^{\prime }=\frac{5N}{5+N}=\frac{5}{\frac{5}{N}+1}$

For $N=5$; $v^{\prime }$ $=2.5m/s$
For $N=10$; $v^{\prime }$ $=10/3m/s$
Also $v^{\prime }$ is never exactly equal to $5m/s.$

From above we can say that increase in speed of the ball is not same every time for collection of each ball in the basket, it varies.