A ball of mass 0.2 kg and radius 0.5 m starting from rest rolls down a 30∘ inclined plane. Find the time in second it would take to cover 7 m

To find the time it would take for the ball to cover 7 m down the inclined plane, we can use the equations of motion.

First, let's find the acceleration of the ball down the inclined plane. The component of the gravitational force acting parallel to the plane can be calculated using the formula:

F_parallel = m * g * sin(theta)

where m is the mass of the ball (0.2 kg), g is the acceleration due to gravity (9.8 m/s^2), and theta is the angle of the inclined plane (30 degrees).

F_parallel = 0.2 kg * 9.8 m/s^2 * sin(30 degrees) F_parallel = 0.2 kg * 9.8 m/s^2 * 0.5 F_parallel = 0.98 N

Next, we can use the equation of motion for linear motion:

s = ut + (1/2) * a * t^2

where s is the distance covered (7 m), u is the initial velocity (0 m/s), a is the acceleration (F_parallel / m), and t is the time we want to find.

Rearranging the equation, we get:

t^2 = (2 * s) / a t^2 = (2 * 7 m) / (0.98 N / 0.2 kg) t^2 = 14 m / (4.9 N/kg) t^2 = 2.857 s^2

Taking the square root of both sides, we find:

t = sqrt(2.857 s^2) t ≈ 1.69 s

Therefore, it would take approximately 1.69 seconds for the ball to cover 7 m down the inclined plane.