Question

Two bodies of masses 4.kg and 16 kg at rest
to acted upon by same force. The ratio of times
required to attain the same speed is,​

Answer 1

Thus the ratio of times to attain the same speed is 1 : 4

Explanation:  

• Velocity for mass 1 kg = v  1
• Taking velocity for mass 4 kg = v2

Given that e1  = e 2

Equating the above terms and simplifying, we get,

Now the momentum is given by:

Momentum for mass 1 kg = p1  

Momentum for 4 kg mass = p2

P1  = 1 × v  1

​and P 2  =4 × v 2

Then

P1 / P2 = 1 / 4 = 1 : 4

Thus the ratio of times to attain the same speed is 1 : 4

​

Answer 2

Given:

F1 = F2 = F

m1 = 4 kg

m2 = 16 kg

To Find:

The ratio of times  required for both bodies to attain the same speed.

Calculation:

- The force is given as:

F1 = m1 a1

⇒ F = 4a1

⇒ a1 =- F/4

- Again, we have:

F2 = m2 a2

⇒ F = 16a2  

⇒ a2 = F/16

- Let the same speed be v.

- Then we have:

v = u + a1 t1

⇒ v = a1 t1  (as u =0)

⇒ v = F t1/4   ...(i)

and v = u + a2 t2

⇒ v = a2 t2  (as u =0)

⇒ v = F t2/16  ...(ii)

- From (i) and (ii), we have:

F t1/4 = F t2/16

⇒ t1/t2 = 4/16

⇒ t1/t2 = 1/4

- So, the ratio of times  required to attain the same speed is 1:4.