A wedge Y with mass of 10 kg and all frictionless surfaces and the inclined surface making with horizontal

Question

A wedge Y with mass of 10 kg and all frictionless surfaces and the inclined surface making $37 °$ with horizontal. A block X with mass 2 kg is placed at the highest point of the wedge as shown in figure is at rest. At $t = 0$ wedge (Y) is pulled toward right with constant force $(f)$ of 24 N. Taking the block X at rest at $t = 0$ , the time taken by it to slide down 8.8 m on the slope, while Y is on the move, is _________ s.

$(Take \tan (37 °) = \frac{3}{4} and g = 10 m / s^{2})$ [2026]

Smart Achievers · Accepted Answer

(1)

$t = 0$

$10 a + 2 [b \cos 37 ° + a] = 24$

$60 a + 8 b = 120$ $. . . (i)$

$NLM on block along inclined plane$

$2 \times 10 \sin 37 ° = 2 [b + a \cos 37 °]$

$\Rightarrow 4 a + 5 b = 30$ $. . . (i i)$

$from (i) and (ii)$

$60 [\frac{30 - 5 b}{4}] + 8 b = 120$

$\Rightarrow b = \frac{330}{67} m s^{- 2}$

$\Rightarrow t = \sqrt{\frac{2 \times 8.8 \times 67}{330}} \approx 2 sec$

Solution

1 $2$

2 $4$

3 $\sqrt{2}$

4 $2 \sqrt{2}$

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