Question

Starting from rest, an object rolls down along an incline Rhat rises by 3 in every 5along it. The object gains a speed√10m/s as it travels a distance of 5/3m along the incline. What can be the possible shapes of object?

Answer 1

Given: An incline that rises by 3 in every 5 along it, object gains a speed √10 m/s as it travels a distance of 5/3 m along the incline.

To find: The possible shapes of object.

Solution:

• Now we have sin (theta) = 3/5.

• The linear distance traveled is given by   s = h/sin(theta).

• Solving further, we get:

             s x sin(theta)  = 5/3 x 3/5 = 1

• Now the formula for velocity of the rolling body is:

             v = $\sqrt{2gh / (1 + (k^2/R^2)}$

• Now we have given the value of v, that is √10 m/s  and h = 1.

• Putting these values in formula, we get:

            10 = 2 x g x 1 / 1 +k^2/R^2

• By solving further, we get:

            1 + k^2/R^2 = 2

            k^2/R^2 = 1

Answer:

                So from this, we can conclude that object must be ring or hollow cylinder.