Question:
The time taken by a body to slide down the smooth inclined plane is \(4\) sec. The time taken by a body to slide \(1/4^{th}\) of the length of the plane is
The time taken by a body to slide down the smooth inclined plane is \(4\) sec. The time taken by a body to slide \(1/4^{th}\) of the length of the plane is
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For uniformly accelerated motion from rest, distance is proportional to \(t^2\).
Updated On: May 7, 2026
- \(1\) sec
- \(2\) sec
- \(3\) sec
- \(0.5\) sec
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The Correct Option is B
Solution and Explanation
Concept:
For motion starting from rest with uniform acceleration: \[ s=\frac{1}{2}at^2 \]
Step 1: Since the plane is smooth, acceleration down the plane is constant.
Step 2: Distance travelled is proportional to square of time: \[ s\propto t^2 \]
Step 3: Let full length of plane be \(L\), and time taken for full length be: \[ T=4\text{ sec} \]
Step 4: For \(1/4\) of the length: \[ \frac{s}{L}=\frac{1}{4} \] \[ \frac{t^2}{T^2}=\frac{1}{4} \]
Step 5: \[ \frac{t}{T}=\frac{1}{2} \] \[ t=\frac{T}{2} \] \[ t=\frac{4}{2}=2\text{ sec} \] \[ \boxed{2\text{ sec}} \]
For motion starting from rest with uniform acceleration: \[ s=\frac{1}{2}at^2 \]
Step 1: Since the plane is smooth, acceleration down the plane is constant.
Step 2: Distance travelled is proportional to square of time: \[ s\propto t^2 \]
Step 3: Let full length of plane be \(L\), and time taken for full length be: \[ T=4\text{ sec} \]
Step 4: For \(1/4\) of the length: \[ \frac{s}{L}=\frac{1}{4} \] \[ \frac{t^2}{T^2}=\frac{1}{4} \]
Step 5: \[ \frac{t}{T}=\frac{1}{2} \] \[ t=\frac{T}{2} \] \[ t=\frac{4}{2}=2\text{ sec} \] \[ \boxed{2\text{ sec}} \]
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