Question

the time taken by a body to slide down the smooth inclined plane in t seconds. then the time taken by it to slide 1/4th of the length of the plane is
a) t/2 seconds
b) t/4 seconds
c) t
d) t/8seconds​

Answer 1

Answer:

Let the height of the inclined plane be h.

Time taken by the body to displace by a height of h = t

We know that,

Time of descent=t=$\sqrt{\frac{2h}{g}}$

Time taken by the body to displace by a height of h/4 =

$\: \: \: \: \: \: \: \: \sqrt{\frac{2×\frac{h}{4}}{g}}\\ \: \: \: \: \: \: \: =\: \sqrt{\frac{2h}{4g}}\\ \: \: \: \: \: \: \: =\: \sqrt{\frac{1}{4}×\frac{2h}{g}}\\ \: \: \: \: \: \: \: =\: \frac{1}{2}\sqrt{\frac{2h}{g}}\\ \: \: \: \: \: \: \: =\: \frac{1}{2}×t \\ \: \: \: \: \: \: \: =\: \frac{t}{2}$

SO OPTION A)t/2 seconds IS CORRECT