Laws of Motion

A body of mass m is suspended by two strings making angles 1 and 2 with the horizontal ceiling with tensions T1 and T2 simultaneously. T1 and T2 are related by T1 = 3T2, the angles 1 and 2 are

1. 1 = 30 , 2 = 60 with T2 = 3mg4
2. 1 = 45 , 2 = 45 with T2 = 3mg4
3. 1 = 30 , 2 = 60 with T2 = 4mg5
4. 1 = 60 , 2 = 30 with T2 = mg2

[figure] A body of mass 1 kg is suspended with the help of two strings making angles as shown in figure. Magnitudes of tensions T1 and T2, respectively, are (in N) : (Take acceleration due to gravity 10 m/s2)

1. 5 3, 5
2. 5 3, 5 3
3. 5, 5
4. 5, 5 3

A balloon and its content having mass M is moving up with an acceleration ‘a’. The mass that must be released from the content so that the balloon starts moving up with an acceleration ‘3a’ will be (Take ‘g’ as acceleration due to gravity)

1. 3Ma2a + g
2. 2Ma3a + g
3. 3Ma2a - g
4. 2Ma3a - g

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