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Question: Two bodies A and B have masses 20 kg and 5 kg respectively. Each one is acted upon by a force of 4 k...

Two bodies A and B have masses 20 kg and 5 kg respectively. Each one is acted upon by a force of 4 kg wt. If they acquire the same kinetic energy in times tA\mathrm { t } _ { \mathrm { A } } and tB\mathrm { t } _ { \mathrm { B } }, then the ratio tAtB\frac { \mathrm { t } _ { \mathrm { A } } } { \mathrm { t } _ { \mathrm { B } } } is :

A

12\frac { 1 } { 2 }

B

2

C

25\frac { 2 } { 5 }

D

56\frac { 5 } { 6 }

Answer

2

Explanation

Solution

Here, m1=20 kg, m2=5 kg\mathrm { m } _ { 1 } = 20 \mathrm {~kg} , \mathrm {~m} _ { 2 } = 5 \mathrm {~kg}

Force = 40 N

∴a1=2 ms−2\therefore \mathrm { a } _ { 1 } = 2 \mathrm {~ms} ^ { - 2 } and a2=8 ms−2\mathrm { a } _ { 2 } = 8 \mathrm {~ms} ^ { - 2 }

12 m1(a1tA)2=12 m2(a2tB)2\frac { 1 } { 2 } \mathrm {~m} _ { 1 } \left( \mathrm { a } _ { 1 } \mathrm { t } _ { \mathrm { A } } \right) ^ { 2 } = \frac { 1 } { 2 } \mathrm {~m} _ { 2 } \left( \mathrm { a } _ { 2 } \mathrm { t } _ { \mathrm { B } } \right) ^ { 2 }

∴12×20×4×tA2=12×5×64×tB2\therefore \frac { 1 } { 2 } \times 20 \times 4 \times \mathrm { t } _ { \mathrm { A } } ^ { 2 } = \frac { 1 } { 2 } \times 5 \times 64 \times \mathrm { t } _ { \mathrm { B } } ^ { 2 }

∴tA2tB2=12×5×6412×20×4=41\therefore \frac { \mathrm { t } _ { \mathrm { A } } ^ { 2 } } { \mathrm { t } _ { \mathrm { B } } ^ { 2 } } = \frac { \frac { 1 } { 2 } \times 5 \times 64 } { \frac { 1 } { 2 } \times 20 \times 4 } = \frac { 4 } { 1 }