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Question

A ball rolls down from the top of a staircase with horizontal velocity 36 m/s. If each step is 4 m high and 3 m wide, the ball just hits the edge of the nth step where n=1152αg , then α is :
[g is the acceleration due to gravity]


A
1
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B
2
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C
3
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D
4
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Solution

The correct option is A 1
Let the horizontal direction be along x axis and vertical direction be along y axis.

Given, the ball just hits the edge of the nth step.

So, total horizontal distance to be covered x=3×n=3n

and total vertical distance to be covered y=4×n=4n

Then, using the kinematic relation, s=ut+12at2

Along horizontal direction :

we can write that, x=uxt+12axt2

3n=uxt [as ax=0]

Given, ux=36 m/s

3n=36t t=3n36 ............(1)

Along vertical direction :

we can write that, y=uyt+12ayt2

From the data given in the question,

4n=12gt2 ...........(2)

From (1) and (2)

4n=12g(3n36)2

n=g8×n2144=n2g1152

n2g1152n=0

n=1152g or n=0 (trivial)

Comparing with n=1152αg, we get
α=1

Hence, option (a) is the correct answer.

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