In the figure given below, the position-time graph of a particle of mass 0.1 Kg is shown. The impulse at t = 2 sec is 

(1) 0.2 kg m sec^–1

(2) –0.2 kg m sec^–1

(3) 0.1 kg m sec^–1

(4) –0.4 kg m sec^–1

The force-time (F – t) curve of a particle executing linear motion is as shown in the figure. The momentum acquired by the particle in time interval from zero to 8 second will be 

(1) – 2 N-s

(2) + 4 N-s

(3) 6 N-s

(4) Zero

A body of 2 kg has an initial speed 5ms^–1. A force acts on it for some time in the direction of motion. The force time graph is shown in figure. The final speed of the body.

(1) 9.25 ms^–1

(2) 5 ms^–1

(3) 14.25 ms^–1

(4) 4.25 ms^–1

A particle of mass m, initially at rest, is acted upon by a variable force F for a brief interval of time T. It begins to move with a velocity u after the force stops acting. F is shown in the graph as a function of time. The curve is an ellipse.

(1) $u=\frac{\pi F_0^2}{2m}$

(2) $u=\frac{\pi T^2}{8m}$

(3) $u=\frac{\pi F_{0}T}{4m}$

(4) $u=\frac{F_{0}T}{2m}$

A body of mass 3kg is acted upon by a force which varies as shown in the graph below. The momentum acquired is given by

(1) Zero

(2) 5 N-s

(3) 30 N-s

(4) 50 N-s

The variation of momentum with the time of one of the bodies in a two-body collision is shown in fig. The instantaneous force is the maximum corresponding to the point:
             
1. \(P\)
2. \(Q\)
3. \(R\)
4. \(S\)

Figures I, II, III and IV depict variation of force with time.

(I)
(II)
(III)
(IV)

The impulse is highest in the case of situations depicted. Figure

(1) I and II

(2) III and I

(3) III and IV

(4) IV only

The masses of 10 kg and 20 kg respectively are connected by a massless spring as shown in figure. A force of 200 N acts on the 20 kg mass. At the instant shown, the 10 kg mass has acceleration 12 m/sec². What is the acceleration of 20 kg mass?

(1) 12 m/sec²

(2) 4 m/sec²

(3) 10 m/sec²

(4) Zero

Two masses M and m are connected by a weightless string. They are pulled by a force F on a frictionless horizontal surface. The tension in the string will be

(1) $\frac{FM}{m+M}$

(2) $\frac{F}{M+m}$

(3) $\frac{FM}{m}$

(4) $\frac{Fm}{M+m}$ 

A uniform rope of length l lies on a table. If the coefficient of friction is μ, then the maximum length l₁ of the part of this rope which can overhang from the edge of the table without sliding down is 

(1) $\frac{l}{\mu }$

(2) $\frac{l}{\mu +l}$

(3) $\frac{\mu l}{1+\mu }$

(4) $\frac{\mu l}{\mu -1}$