First slide

Rectilinear Motion

Question

A body sliding on a smooth inclined plane requires 4 s to reach the bottom, starting from rest at the top. How much time does it take to cover one-fourth the distance starting from rest at the top?

Moderate

A

1s
B

2s
C

4s
D

16s

Solution

When a body slides on an inclined plane, component of weight along the plane produces an acceleration.
$a = \frac{m g \sin θ}{m} = g \sin θ = Constant$
If s is the length of the inclined plane, then
$\begin{array}{l} s = 0 + \frac{1}{2} a t^{2} = \frac{1}{2} g \sin θ \times t^{2} \\ \frac{s^{'}}{s} = \frac{t^{' 2}}{t^{2}} or \frac{s}{s^{'}} = \frac{t^{2}}{t^{' 2}} \\ Given t = 4 s and s^{'} = \frac{s}{4} \\ t^{'} = t \sqrt{\frac{s^{'}}{s}} = 4 \sqrt{\frac{s}{4 s}} = \frac{4}{2} = 2 s \end{array}$

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