Two identical charged spheres suspended from a  common point by two massless strings of lengths l, are initially at a distance d (d < l) apart because of their mutual repulsion. The charges begin to leak from both the spheres at a constant rate. As a result, the spheres approach each other with a velocity v. Then, v varies as a function of the distance x between the sphere, as

• vx

• 

• vx^-1

• 

A ship A is moving Westwards with a speed of 10 kmh^-1 and a ship B 100km  south of A, is moving Northwards with a speed of 10 kmh^-1. The time after which the distance between them becomes shortest is

• 0 h

• 5 h

• 
• 

A particle is moving such that its position coordinates (x,y) are (2m, 3m) at time t = 0, (6m, 7m) at time t = 2 sec and (13 m, 14m) at time t= 5 sec. Average velocity vector (v_av) from t = 0 to t = 5 s is,

The force F acting on a particle of mass m is indicated by the force-time graph as shown below. The climate change in momentum of the particle over the time interval from zero to 8 s is,

• 24 Ns

• 20 Ns

• 12 Ns

• 12 Ns

The motion of a particle along a straight line is described by equation
 x=8+12 t -t³

where x is in metre and t in second. The retardation of the particle when its velocity becomes zero, is

• 24 ms^-2

• zero

• 6 ms^-2

• 6 ms^-2

A stone falls freely under gravity. It covers distances h₁ , h₂ and h₃ in the first 5 seconds, the next 5 seconds and the next 5 seconds respectively. The relations between h₁, h₂ and h₃ is,

• h₁ = 2 h₂ = 3 h₃

• h₁ = 

• h₂ = 3 h₁ and h₃ = 3 h₂

• h₂ = 3 h₁ and h₃ = 3 h₂

Three blocks will masses m, 2m and 3m are connected by strings, as shown in the figure. After an upward force F is applied on block m, the masses move upward at constant speed v. What is the net force on the block of mass 2m? (g is the acceleration due to gravity)

• zero

• 2 mg

• 3 mg

• 3 mg

A uniform force of (3 i + j) N acts on a particle of mass 2 kg. Hence the particle is displaced from position (2 i + k) m to position ( 4 i + 3 j - k) m. The work done by the force on the particle is,

• 9 J

• 6 J

• 13 J

• 13 J

99.

A plank with a box on it at one end is gradually raised about the other end. As the angle of inclination with the horizontal reaches 30^o, the box starts to slip and slides 4.0 m down the plank in 4.0 s. The coefficients of static and kinetic friction between the box and the plank will be respectively

• 0.6 and 0.6

• 06 and 0.5

• 0.5 and 0.6 

• 0.4 and 0.3

A particle covers half of its total distance with speed v₁ and the rest half distance with speed v₂. Its average speed during the complete journey is

• v₁v₂ / v₁ + v₂

• 2v₁v₂/v₁ + v₂

• 2v₁²v²₂ / v₁² + v²₂

• 2v₁²v²₂ / v₁² + v²₂