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

A heavy uniform chain lies on a horizontal table-top. If the coefficient of friction between the chain and table surface is 0.25, then the maximum fraction of length of the chain, that can hang over one edge of the table is 

(1) 20%

(2) 25%

(3) 35%

(4) 15%