A barbell consists of two identical masses, each of mas m, at the end of a massl

Question

A barbell consists of two identical masses, each of mas m, at the end of a massless rod. We will treat the masses as point masses. The barbell is then rotated in a plane (in two dimensions ) about a point along the rod which is a distance L1 from one mass and L2 from the other. The barbell rotates at a constant angular velocity. Which of the following statements is correct?

A. The kinetic energy of the barbell is 0.5*m*(L12 + L22)*w2. The masses rotate at different linear speeds.

B. The kinetic energy of the barbell is 0.5*m*L2*w2, since the masses rotate at the same linear speed and L is the length of the barbell.

C. The kinetic energy of the barbell is 0.5*m*(L12 + L22)*w2. The masses rotate at the same linear speed, since they rotate together.

D. The kinetic energy of the barbell is 0.5*I*w2 , where I, the moment of inertia, is mL2. Here, L is the length of the rod.

Explanation / Answer

If there is pure rotation,kinetic energy is given as

KE=0.5*I*w*w

I=(m(L1^2+L2^2)

KE=0.5*m*(L1^2+L2^2)*w^2

Linear speed is w*L

So L1is not equal to L2 ,linear speed will be different

So option (A) is correct

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