Laws of Motion · Question 15

A 4 kg mass moves under the influence of a force F = (4t3 i - 3t j) N where t is the time in second. If mass starts from origin at t = 0, the velocity and position after t = 2 s will be:

1. v = 3 i + 32 j r = 65 i + j
2. v = 4 i - 32 j r = 65 i - j
3. v = 4 i - 32 j r = 85 i - j
4. v = 4 i + 52 j r = 85 i + 2 j

A large drum having radius R is spinning around its axis with angular velocity , as shown in figure. The minimum value of so that a body of mass M remains stuck to the inner wall of the drum, taking the coefficient of friction between the drum surface and mass M as , is : [figure]

1. 2g R
2. g2 R
3. gR
4. g R

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