Question

31. Two spheres whose radii are in the ratio 1 : 2
are moving with their velocities in the ratio
3:4. If their densities are in the ratio 3:2. the
ratio of their kinetic energies is,
1) 27 : 64 2) 1:1 3) 27 : 256 4) 9 : 64​

Answer 1

answer : option (3) 27 : 256

ratio of radii of two spheres = 1 : 2

ratio of volumes = (1/2)³ = 1 : 8

ratio of their densities = 3 : 2

so, ratio of their masses = ratio of densities × ratio of volumes of it

= (3/2) × (1/8)

= 3/16

now kinetic energy = 1/2 mv²

so, ratio of kinetic energies of given spheres = ratio of their masses × (ratio of their velocities)²

= (3/16) × (3/4)²

= 3/16 × 9/16

= 27/256

hence, ratio of kinetic energies is 27 : 256

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Answer 2

Answer:

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