Consider elastic collision of a particle of mass m moving with a velocity u with another particle of the same mass at rest. After the collision the projectile and the struck particle move in directions making angles θ₁ and θ₂ respectively with the initial direction of motion. The sum of the angles. θ₁ + θ₂, is 

(1) 45°

(2) 90°

(3) 135°

(4) 180°

A batsman hits a sixer and the ball touches the ground outside the cricket field. Which of the following graph describes the variation of the cricket ball's vertical velocity v with time between the time t₁ as it hits the bat and time t₂ when it touches the ground 

(1)

(2)

(3)

(4)

The relationship between force and position is shown in the given figure (in a one-dimensional case). The work done by the force in displacing a body from \(x = 1\) cm to \(x = 5\) cm is:

1.   \(20\) ergs
2.   \(60\) ergs
3.   \(70\) ergs
4.   \(700\) ergs

The pointer reading v/s load graph for a spring balance is as given in the figure. The spring constant is-

(1) 0.1 N/cm

(2) 5 N/cm

(3) 0.3 N/cm

(4) 1 N/cm

Adjacent figure shows the force-displacement graph of a moving body, the work done in displacing body from x = 0 to x = 35 m is equal to-

(1) 50 J

(2) 25 J

(3) 287.5 J

(4) 200 J

A 10kg mass moves along x-axis. Its acceleration as a function of its position is shown in the figure. What is the total work done on the mass by the force as the mass moves from x = 0 to x = 8 cm ?

(1) 8 × 10^–2 joules

(2) 16 × 10^–2 joules

(3) 4 × 10^–4 joules

(4) 1.6 × 10^–3 joules

A toy car of mass 5 kg moves up a ramp under the influence of force F plotted against displacement x. The maximum height attained is given by

(1) y_max = 20 m

(2) y_max = 15 m

(3) y_max = 11 m

(4) y_max = 5 m

The graph between the resistive force \(F\) acting on a body and the distance covered by the body is shown in the figure. The mass of the body is \(25\) kg and the initial velocity is \(2\) m/s. When the distance covered by the body is \(4\) m, its kinetic energy would be:

   
1.   \(50\) J
2. \(40\) J
3. \(20\) J
4.   \(10\) J

A particle of mass 0.1 kg is subjected to a force which varies with distance as shown in fig. If it starts its journey from rest at x = 0 , its velocity at x = 12 m is 

(1) 0 m/s

(2) $20\sqrt{2}m/s$

(3) $20\sqrt{3}m/s$

(4) 40 m/s

The relation between the displacement \(X\) of an object produced by the application of the variable force \(F\) is represented by a graph (as shown in the figure below). If the object undergoes a displacement from \(X=0.5\) m to \(X=2.5\) m the work done will be approximately equal to: 

    
1. 16 J
2. 32 J
3. 1.6 J
4. 8 J