Laws of Motion

A body of mass 2 kg moving with velocity of vin = 3 i + 4 j m s-1 enters into a constant force field of 6 N directed along positive z-axis. If the body remains in the field for a period of 53 seconds, then velocity of the body when it emerges from the force field is:

1. 3 i + 4 j + 5 k
2. 4 i + 3 j + 5 k
3. 3 i + 4 j - 5 k
4. 3 i + 4 j + 5 k

A cubic block of mass m is sliding down on an inclined plane at 60 with an acceleration of g2, the value of coefficient of kinetic friction is

1. 32
2. 23
3. 1 - 32
4. 3 - 1

An object with mass 500 g moves along x-axis with speed v = 4 x m/s. The force acting on the object is :

1. 8 N
2. 4 N
3. 5 N
4. 6 N

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 .