A body sliding on a smooth inclined plane requires 4 seconds to reach the bottom starting from rest at the top. How much time does it take to cover one-fourth distance starting from rest at the topa)1 sb)2 sc)4 sd)16 sCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

Answer

Answer

Use s=1/2 gt^2
s= 1/2×10 ×16
s=80
1/4s=20
20=1/2gt^2
t=√(2×20/10)=√4
t=2s

note s is the perpendicular height of inclined plane

Answer

Given:
- A body sliding on a smooth inclined plane
- The body requires 4 seconds to reach the bottom starting from rest at the top

To find:
- How much time does it take to cover one-fourth distance starting from rest at the top

Solution:
To solve this problem, we can use the equations of motion for uniformly accelerated motion.

1. Time to reach the bottom:
Let's denote the time taken to reach the bottom as t1. Using the equation of motion for uniformly accelerated motion:

s = ut + (1/2)at^2

Since the body starts from rest, the initial velocity u is 0. The distance s is the full distance covered by the body, and we can denote it as S. The acceleration a can be calculated using the inclined plane's angle of inclination θ.

For a body sliding on a smooth inclined plane, the acceleration can be calculated using the formula:

a = g*sin(θ)

where g is the acceleration due to gravity.

Therefore, the equation becomes:

S = (1/2)gt1^2

2. Time to cover one-fourth distance:
Let's denote the time taken to cover one-fourth distance as t2. The distance covered is one-fourth of the full distance, so we can denote it as S/4.

Using the same equation of motion, we have:

S/4 = (1/2)gt2^2

We need to find t2.

3. Comparing t1 and t2:
To find the relationship between t1 and t2, we can divide the equation for t2 by the equation for t1:

(S/4) / S = ((1/2)gt2^2) / ((1/2)gt1^2)

Simplify the equation:

1/4 = t2^2 / t1^2

Taking the square root of both sides:

1/2 = t2 / t1

Therefore, t2 = (1/2)t1

Since t1 is given as 4 seconds, we can substitute this value into the equation to find t2:

t2 = (1/2) * 4 = 2 seconds

Answer:
The time it takes to cover one-fourth distance starting from rest at the top is 2 seconds. Therefore, the correct answer is option B.

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