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JEE Advanced 2006

Exam: JEE Advanced
Year: 2006
Subject: Physics
Chapter: Center of Mass, Momentum and Collision

JEE Advanced 2006 · Physics · Center of Mass, Momentum and Collision

There is a rectangular plate of mass M ~kg of dimensions (a × b) ....

There is a rectangular plate of mass

M \mathrm{~kg}

of dimensions

(a \times b)

. The plate is held in horizontal position by striking

n

small balls 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 \mathrm{~kg}, m=0.01 \mathrm{~kg}

;

b=2 \mathrm{~m} ; a=1 \mathrm{~m} ; g=10 \mathrm{~m} / \mathrm{s}^2

.

There is a rectangular plate of mass M ~kg of dimensions (a × b) . The plate is held in horizontal position by striking

Correct answer

10

Step-by-step solution

F=\frac{\Delta p}{\Delta t}=n \times\left(a \times \frac{b}{2}\right) \times(2 m v)

Equating the torque about hinge side, we have n

\times\left(

a

\times \frac{b}{2}\right) \times(

2 m v)

\times \frac{3 b}{4}=

M g

\times \frac{b}{2}

Substituting the given values we get, v=10

\mathrm{~m}

/

\mathrm{s}

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