Two objects A and B of mass 2 kg and 3 kg, respectively, were dropped from different heights. A took 5 second and B took 3 seconds to touch the ground. What is the ratio of their kinetic energy with which they hit the ground?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 50/27.
To find the ratio of kinetic energies of objects A and B when they hit the ground, we use the formula:
KE = 1/2 mv2
For free-falling objects, v = gt, so:
KE =1/2 m(gt)2 = 1/2 mg2t2
For A: mA = 2 kg , tA = 5 s → KEA=1/2 ⋅ 2 ⋅ g2 ⋅ 52 = 25g2
For B: mB = 3 kg , tB = 3 s → KEB=1/2 ⋅ 3 ⋅ g2 ⋅ 32 = 13.5g2
Ratio KEA : KEB = 25 : 13.5 =50 : 27