Laws of Motion

A car of mass 'm' moves on a banked road having radius 'r' and banking angle . To avoid slipping from banked road, the maximum permissible speed of the car is v0. The coefficient of friction between the wheels of the car and the banked road is

1. = v02+rg rg+v02
2. = v02-rg rg-v02
3. = v02-rg rg+v02
4. = v02+rg rg-v02

[figure] A string of length L is fixed at one end and carries a mass of M at the other end. The mass makes ( 3 ) rotations per second about the vertical axis passing through end of the string as shown. The tension in the string is ML.

A tube of length 1 m is filled completely with an ideal liquid of mass 2M, and closed at both ends. The tube is rotated uniformly in horizontal plane about one of its ends. If the force exerted by the liquid at the other end is F then angular velocity of the tube is F M in SI unit. The value of is .

A light unstretchable string passing over a smooth light pulley connects two blocks of masses m1 and m2. If the acceleration of the system is g8, then the ratio of the masses m2m1 is :

1. 5 : 3
2. 8 : 1
3. 9 : 7
4. 4 : 3

A nucleus at rest disintegrates into two smaller nuclei with their masses in the ratio of 2 : 1. After disintegration they will move :

1. in opposite directions with speed in the ratio of 1 : 2 respectively.
2. in the same direction with same speed.
3. in opposite directions with speed in the ratio of 2 : 1 respectively.
4. in opposite directions with the same speed.

A 1 kg mass is suspended from the ceiling by a rope of length 4 m. A horizontal force 'F' is applied at the mid point of the rope so that the rope makes an angle of 45 with respect to the vertical axis as shown in figure. The magnitude of F is : (Assume that the system is in equilibrium and g = 10 m/s2) [figure]

1. 1 N
2. 10 N
3. 10 2 N
4. 110 2 N

A stationary particle breaks into two parts of masses mA and mB which move with velocities vA and vB respectively. The ratio of their kinetic energies (KB : KA) is :

1. vB : vA
2. 1 : 1
3. mB vB : mA vA
4. mB : mA

A player caught a cricket ball of mass 150 g moving at a speed of 20 m/s. If the catching process is completed in 0.1 s, the magnitude of force exerted by the ball on the hand of the player is:

1. 150 N
2. 3 N
3. 30 N
4. 300 N

A given object takes n times the time to slide down 45 rough inclined plane as it takes the time to slide down an identical perfectly smooth 45 inclined plane. The coefficient of kinetic friction between the object and the surface of inclined plane is :

1. 1 - 1n2
2. 1 - 1n2
3. 1 - n2
4. 1 - n2

A circular table is rotating with an angular velocity of rad/s about its axis (see figure). There is a smooth groove along a radial direction on the table. A steel ball is gently placed at a distance of 1 m on the groove. All the surfaces are smooth. If the radius of the table is 3 m, the radial velocity of the ball w.r.t. the table at the time ball leaves the table is x 2 m/s, where the value of x is . [figure]