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Applying NLM along 3 Axis

A stationary ...

Question

A stationary body of mass m is slowly lowered onto a massive long platform of mass M (>> m) moving at a speed 4 m/s as shown in the figure. How far the body slides along the platform?
[Take = 0.2 and $g = 10 m / s^{2}$ ].

8 m

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12 m

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6 m

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4 m

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Solution

The correct option is D 4 m
Draw the free body diagram of block and platform. As M >> m, the acceleration of the platform, $a = \frac{μ m g}{M}$ can be taken as zero and hence its velocity remains constant as 4m/s. Acceleration of the block is,
${\to a}_{b l o c k, p l a t f o r m} = 2 m / s^{2}$ (towards right)
${\to v}_{b l o c k, p l a t f o r m} = (2 t - 4) m / s$ (towards right)
Initial velocity of block wrt platform is 4 m/s towards left.
Let s be the required distance, then $v^{2} = u^{2} + 2 \to a . \to s \Rightarrow 0 = (- 4)^{2} + 2 (2) s \Rightarrow s = 4 m .$

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A stationary body of mass m is slowly lowered onto a massive long platform of mass M (>> m) moving at a speed 4 m/s as shown in the figure. How far the body slides along the platform? [Take = 0.2 and g=10m/s2].

A stationary body of mass m is slowly lowered onto a massive long platform of mass M (>> m) moving at a speed 4 m/s as shown in the figure. How far the body slides along the platform?
[Take = 0.2 and $g = 10 m / s^{2}$ ].