Question

In the demonstration of a stunt, two solid balls of equal density and radii rand 2, are
placed with the centre of the larger one above the middle of a cart of mass M = 6 kg and
length L = 3 m. The mass of the smaller ball is m = 1 kg. The balls are made to roll,
without slipping in such a way that a straight line connecting their centres remains at
a constant angle 0) = 53° to the horizontal. The cart is pulled by a horizontal force. Find
thetimetaken for the balls to fall of the edge of the cart, in seconds(Take g = 10 m/s)​

Answer 1

Explanation:

Given,

Two balls, each of radius R and of equal mass and density, are placed in contact.

Step-1:

Find the Distance between the centre of two balls

Distance between the centre of two balls = Sum of their Radii.

Distance between the centre of two balls =R+R=2R.

Step-2:

Express the Mass of a ball as product of Density and Volume.

(This would be same for other ball ,given that two balls have equal mass)

Since, the shape of the ball is Sphere.

Volume of the ball V=34πR3

So,

Mass of the ball m=ρ×34πR3

Step-3:

Find the force of gravitation between the two balls.

According to Newton's Law of Universal Gravitation

F=r2GMm

Where,

F= Gravitational Force between two objects.

G= Gravitational constant

M= Mass of the first object

m= Mass of the second object

r= Distance between objects

Here,

.

M=m=ρ×34πR3

Substituting Values

⟹F=(2R)2Gm2

⟹F=4R2G(ρ×34πR3)2

⟹F=G×ρ2×(34)2×41×R2