Centre Of Mass Ques 73
- There is a rectangular plate of mass $M kg$ of dimensions $(a \times b)$. The plate is held in horizontal position by striking $n$ small balls uniformly each of mass $m$ per unit area per unit time.These are striking in the shaded half region of the plate. The balls are colliding elastically with velocity $v$. What is $v$ ?
It is given $n=100, M=3 kg, m=0 \cdot 01 kg$;
$b=2 m ; a=1 m ; g=10 m / s^{2}$.
(2006, 6M)
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Answer:
Correct Answer: 73.$10 m / s$
Solution:
Formula:
Motion of Centre of Mass and Conservation of Momentum:
- $F=\frac{\Delta p}{\Delta t}=n \times a \times \frac{b}{2} \times(2 m v)$
Equating the torque about hinge side, we have
$$ n \times a \times \frac{b}{2} \times(2 m v) \times \frac{3 b}{4}=M g \times \frac{b}{2} $$
Substituting the given values, we get
BETA
