## Tuesday, October 14, 2008

### Questions (MCQ) on Newton’s Laws

The following simple questions may prompt you to pick out the wrong option if you are in a hurry. So, be cautious and don’t overlook basic points. Here are the questions:

(1) Two identical frictionless pulleys carry the same mass 2m at the left ends of the light inextensible strings passing over them. The right end of the string carries a mass 3m in the case of arrangement (i) where as a force of 3mg is applied in the case of arrangement (ii) as shown in the adjoining figure. The ratio of the acceleration of mass 2m in case (i) to the acceleration of mass 2m in case (ii) is (a) 2:3

(b) 1:1

(c) 5:3

(d) 3:5

(e) 2:5

In both cases the net driving force is 3mg – 2mg = mg. But in case (i) the total mass moved is 5m where as in case (ii) the total mass moved is 2m. The acceleration in case (i) is mg/5m = g/5 where as the acceleration in case (ii) is mg/2m = g/2.

The ratio of accelerations = (g/5)/ (g/2) = 2/5 [Option (e)].

(2) An object of mass 4 kg moving along a horizontal surface with an initial velocity of 2 ms–1 comes to rest after 4 seconds. If you want to keep it moving with the velocity of 2 ms–1, the force required is

(a) zero

(b) 1 N

(c) 2 N

(d) 4 N

(e) 8 N

The acceleration ‘a’ of the body is given by

0 = 2 + a×4, on using the equation, vt = v0 + at

Therefore, a = – 0.5 ms–2

The body is retarded (as indicated by the negative sign) because of forces opposing the motion. The opposing force has magnitude ma = 4×0.5 = 2 N. Therefore, a force of 2 N has to be applied opposite to the opposing forces to keep the body moving with the velocity of 2 ms–1.

You will find some useful multiple choice questions (with solution) in this section here as well as here