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Standard XII

Physics

Impulsive Forces in Collision

A block of ma...

Question

A block of mass $1$ kg and a pan of equal mass are connected by a string going over a smooth light pulley. Initially the system is at rest when a particle of mass $1$ kg falls on the pan and stick to it. If the particle strike the pan with speed $6 m / s$ then the speed with which the system moves just after the collision is?

3 m / s

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4 m / s

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2.5 m / s

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2 m / s

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Solution

The correct option is D $2 m / s$
Let the speed of block-pan system is v.
Using impulse momentum theorem
For particle
$J_{1} = m v_{1} - m v = 1 \times 6 - 1 v = 6 - v$ .........(i)
For pan $J_{1} - J_{2} = m v = 1 v = v$ ............(ii)
For block $J_{2} = m v = 1 \times v = v$ .............(iii)
From Eqs. (i), (ii) and (iii)
$v = 6 - v - v$
$\Rightarrow 3 v = 6 \Rightarrow v = \frac{6}{3} = 2 m / s$ .

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The correct option is D 2m/sLet the speed of block-pan system is v.Using impulse momentum theoremFor particleJ1=mv1−mv=1×6−1v=6−v .........(i)For pan J1−J2=mv=1v=v ............(ii)For block J2=mv=1×v=v .............(iii)From Eqs. (i), (ii) and (iii)v=6−v−v⇒3v=6⇒v=63=2m/s.