Laws of Motion

A 0.5 kg mass is in contact against the inner wall of a cylindrical drum of radius 4 m rotating about its vertical axis. The minimum rotational speed of the drum to enable the mass to remain stuck to the wall (without falling) is 5 rad/s. The coefficient of friction between the drum's inner wall surface and mass is . (Take g=10 m/s2)

1. 0.1
2. 0.5
3. 0.7
4. 0.3

A block of mass 5 kg is moving on an inclined plane which makes an angle of 30 with the horizontal. Friction coefficient between the block and inclined plane surface is 32. The force to be applied on the block so that the block will move down without acceleration is N. (g = 10 m/s2).

1. 25
2. 12.5
3. 15
4. 7.5

A small block of mass m slides down from the top of a frictionless inclined surface, while the inclined plane is moving towards left with constant acceleration a0. The angle between the inclined plane and ground is and its base length is L. Assuming that initially the small block is at the top of the inclined plane, the time it takes to reach the lowest point of the inclined plane is . [figure]

1. 2Lg - a0
2. 4Lg 2 - a0(1 + 2 )
3. 2Lg 2 - a0(1 + 2 )
4. 4Lg 2 - a0

In the given figure the blocks A, B and C weigh 4 kg, 6 kg and 8 kg respectively. The coefficient of sliding friction between any two surfaces is 0.5. The force F required to slide the block C with constant speed is N. (Use g = 10 m/s2) [figure]

A flexible chain of mass m hangs between two fixed points at the same level. The inclination of the chain with the horizontal at the two points of support is 30 . Considering the equilibrium of each half of the chain, the tension of the chain at the lowest point is .

1. mg
2. 32mg
3. 12mg
4. 3mg

A block is sliding down on an inclined plane of slope and at an instant t = 0 this block is given an upward momentum so that it starts moving up on the inclined surface with velocity u. The distance (S) travelled by the block before its velocity becomes zero, is . (g = gravitational acceleration)

1. 2u2g
2. u2 2g
3. u22g
4. u22g

A body of mass 14 kg initially at rest explodes and breaks into three fragments of masses in the ratio 2 : 2 : 3. The two pieces of equal masses fly off perpendicular to each other with a speed of 18 m/s each. The velocity of the heavier fragment is m/s.

1. 24 2
2. 12
3. 12 2
4. 10 2

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