The ratio of the accelerations for a solid sphere (mass m and radius R) rolling down an incline of angle  without slipping and slipping down the incline without rolling is,

• 5:7

• 2:3

• 2:5

• 2:5

A car of mass 1000 kg negotiates a banked curve of radius 90m on a frictionless road. If the banking angle is 45^o, the speed of the car is 

• 20 ms^-1

• 30ms^-1

• 5 ms^-1

• 5 ms^-1

Two sphere A and B of masses m₁ and m₂ respectively collide. A is at rest initially and B is moving with velocity v along the x -axis. After the collision, B has a velocity v/2 in a direction perpendicular to the original direction. The mass A moves after collision in the direction

• same as that of B

• opposite to that of B

• 
• 

The upper half of an inclined plane of the inclination  is perfectly smooth while lower half is rough. A block starting from rest at the top of the plane will again come to rest at the bottom, if the coefficient of friction between the block and lower half of the plane is given by,

An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right angles to each other. The first part of mass 1 kg moves with a speed of 12 m/s and the second part of mass 2 kg moves with second part of mass 2 kg moves with 8 m/s speed. If the third part flies off with 4 m/s speed, then its mass is,

• 3 kg

• 5 kg

• 7 kg

• 7 kg

A person of mass 62 kg is inside of a lift of mass 940 kg and presses the button on control panel. The lift starts moving upwards with an acceleration 1.0 m/s². If g = 10 m/s² ,the tension in the supporting cable is

• 9680 N

• 11000 N

• 1200 N 

• 1200 N 

A planet moving along an elliptical orbit is closer to the sun at a distance r₁ and farthest away at a distance of r₂. if v₁ and v₂ are the linear velocities at these points respectively, then the ratio v₁/v₂ is

• r₂/r₁

• (r₂/r₁)²

• r₁ /r₂

• r₁ /r₂

Force F on a particle moving in a straight line varies with distance d as shown in the figure. The work done on the particle during its displacement of 12 m is

• 21 J

• 26 J 

• 13 J

• 13 J

Uniform magnetic field acting along AB. If the magnetic force on the arm BC Is F, the force on the arm AC is

• -F
• F
• 
• 

120.

Two stone of masses m and 2m are whirled in horizontal circles, the heavier one in a radius r/2 and the lighter one in radius r. The tangential speed of lighter one in radius r. The tangential speed of lighter stone is n times that of the value of heavier stone when they experience same centripetal forces. The value of n is

• 2

• 3

• 4

• 4