Question

A force of 100 N acts on 50 kg for 2 seconds. The same force acts on 25 legs for 2 seconds. The ratio of the momenta produced, and the accelerations caused in two bodies respectively are - (A) 1 : 1, 2: 1 (B) 1 : 1, 1: 2 (C) 1 : 2, 1 : 1 (D) none of these​

Answer 1

Answer:

Correct option is

C

500 m s  

−1

 

Given :   F=100 N      m=2 kg       t=10 s

Change in momentum of the body   m(Δv)=F.t

where Δv is the change in velocity.

⟹ 2×Δv=100×10

⟹ Δv=500 m/s

Explanation:

Answer 2

Answer: The correct option is (B) 1:1, 1:2

Explanation:

The product of the force and the time for which it acts gives the momentum produced in an object by a force:

p = F*t

The acceleration caused by a force in an object is given by the product of the force and the inverse of the object's mass:

a = F/m

Let us apply these equations to determine the momentum and acceleration of the two objects.

For the first object weighing 50 kg:

The resulting momentum is:

p1 = F*t = 100 N * 2 s = 200 Ns

The resulting acceleration is:

a1 = F/m = 100 N/kg = 2 m/s2

For the second object, which weighs 25 kg:

The resulting momentum is:

100 N * 2 s = 200 Ns p2 = F*t

The resulting acceleration is:

a2 = F/m = 100 N/kg = 4 m/s2

The produced momenta ratio is:

200 Ns / 200 Ns = 1 p1/p2

The acceleration ratio caused is:

a1/a2 = 2 m/s2/4 m/s2 = 1/2

As a result, the ratio of produced momenta is 1:1, and the ratio of caused accelerations is 1:2.

As a result, the correct answer is (B)1:1,1: 2.

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