Question

A solid sphere is in rolling motion. In rolling motion
a body possesses translational kinetic energy (K)
as well as rotational kinetic energy (K)
simultaneously. The ratio K, : (K, + K) for the
sphere is
[NEET-2018]
(1) 7:10
(2) 5:7
(3) 2:5
(4) 10:7​

Answer 1

In this case, the second option i.e. 5:7 is the right option for this answer.

When a solid sphere is in motion, it exhibits Translational kinetic energy as well as Translational kinetic energy.

So the resultant ratio will be the ratio of these two forms of energy and upon computation,it would result into 5:7. when 1/2mvm2 will be divided by (1/2+1/5)mv2.

So the right answer in this case would be option (2) i.e. 5:7.

Answer 2

Answer:

5/7

Explanation:

In rolling motion the translational kinetic energy is equal to ;

Kt = ½ mv^2

In rolling motion the rotational kinetic energy is equal to ;

Kr = ½ Iw^2

Kr =  ½ Iw^2 = ½(2/5mr^2)(v/r)^2

Kt + Kr  = ½ mv^2 + ½ Iw^2

Kt + Kr  = ½ mv^2 + ½(2/5mr^2)(v/r)^2

Kt + Kr  = 7/10mv^2

Kt/(kt + Kr) = (½ mv^2)⁄(7/10mv^2)

Solving and simplifying above ; we get

Kt/(kt + Kr) = 5/7