1

Question

Two inclined frictionless tracks, one gradual and the other steep meet at A from where two stones are allowed to slide down from rest, one on each track (Fig. 6.16). Will the stones reach the bottom at the same time? Will they reach there with the same speed? Explain. Given θ₁ = 300, θ₂ = 600, and h = 10 m, what are the speeds and times taken by the two stones ?

Open in App

Solution

Given, the angle of gradual inclined track is

The following diagram shows two stones at the inclined tracks.

Here,

The initial potential energy of the stones is same for both and is given by,

Here,

This potential energy of each stone is converted into the final kinetic energy of the stones as there is no frictional resistance on the tracks, therefore,

Here,

The above expression shows that the final speed of both the stones will be same.

Let

Here,

Let

Here,

It is given that

Let

Then from equation of motion,

When initial velocity is

From the above expression, time is inversely dependent on acceleration. Hence, from equation (4) and equation (3),

Here,

Thus, the above expression shows that time taken by stone

Hence, as the time taken by stone at steeper track is less than that of the other, it will reach the bottom earlier and the speed of both the stones at the bottom will be same (

0

View More

Join BYJU'S Learning Program

Join BYJU'S Learning Program