Two objects, X and Y, are held at rest on a horizontal frictionless surface and a spring is compressed between them. The mass of X is half of the mass of Y. Immediately after the spring is released, X has a kinetic energy of 30 J and Y has a kinetic energy of:A. 45 J B. 7.5J C. 30 J D. 15 J E. 60 J

Answer: (E) 60J

Explanation:

According to the question

Mx = My/2

2Mx = My

(Where Mx is the mass of X and My is the mass of Y)

Y is twice as heavy as X

Kinetic energy of an object =

1/2mv^2

Kinetic energy of X

Ex = 1/2Mx. V^2 ... Eqn 1

Where V is the velocity

(We assume that the velocity is equal for both objects, there is absence of friction. They have been set in motion by force from the same spring)

Kinetic energy for Y

Ey = 1/2My. V^2 ... eqn 2

But My = 2Mx

Ey = 1/2 (2Mx. V^2)

Ey = Mx. V^2 ... eqn 3

From eqn 1

Ex = 30

30 = 1/2Mx. V^2

Multiply through by 2

60 = Mx. V^2

Mx = 60 (V^-2) ... eqn 4

Put eqn 4 in eqn 3

Replace the value of Mx

Ey = 60 (V^-2). V^2

Ey = 60 (V^-2+2)

Ey = 60J