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A block is placed on an inclined plane moving towards right horizontally with an acceleration a₀ = g. The length of the plane AC = 1m. Friction is absent everywhere. The time taken by the block to reach from C to A is (g = 10 m/s²)

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a

1.2 s

b

2.56 s

c

0.42 s

d

0.74 s

answer is B.

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Detailed Solution

Drawing free body diagram of block with respect to plane.

Question Image

Acceleration of the block up the plane is

$a = \frac{mgcos 30^{\circ} - mgsin 30^{\circ}}{m} = (\frac{\sqrt{3} - 1}{2}) g = 3 .66 m / s^{2}$

$\begin{array}{l} Applying s = \frac{1}{2} {at}^{2} \\ t = \sqrt{\frac{2 s}{a}} = \sqrt{\frac{2 \times 1}{3 .66}} = 0 .74 s \end{array}$

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A block is placed on an inclined plane moving towards right horizontally with an acceleration a0 = g. The length of the plane AC = 1m. Friction is absent everywhere. The time taken by the block to reach from C to A is (g = 10 m/s2)