Laws of Motion

A car moving with a speed of 54 km/h takes a turn of radius 20 m. A simple pendulum is suspended from the ceiling of the car. Determine the angle made by the string of the pendulum with the vertical during the turning. (Take g=10 m/s2)

1. -1(0.5)
2. -1(0.75)
3. -1(1.125)
4. -1(0.25)

Two blocks (P and Q) with respectively masses 2 kg and 1.5 kg are joined by a massless thread. These blocks are mounted on a frictionless pulley which is fixed on the edge of a cube (S), as shown in the figure below. Block P is positioned on the top surface which has no friction and block Q is in contact with side-surface, having coefficient of friction . The cube (S) moves towards the right with acceleration of g2, where g is gravitational acceleration. During this movement the block P and Q remain stationary. The value of is . (take g = 10 m/s2) [figure]

1. 0.33
2. 0.67
3. 1
4. 0.5

The velocity at which 6 kg mass (shown in figure) strikes the ground when it is released from a height of 6 m above the ground is m/s. Assume pulley is massless and string is light and inextensible. (Take g = 10 m/s2) [figure]

1. 7.74
2. 7.20
3. 6.55
4. 4.50

A block takes t time to slide down a plane inclined at 45° to the horizontal. If the surface is made smooth (frictionless), the block takes time t2 to slide down the plane. The coefficient of friction between the block and the inclined plane is ( 100 ). The value of is .

Three masses m1=4 kg, m2=4 kg and m3=6 kg are suspended from a fixed smooth frictionless pulley as shown in the figure below. The value of T1/T2 is . (take g=10 m/s2) [figure]

1. 5/3
2. 2/3
3. 3/5
4. 2/5

A wedge Y with mass of 10 kg and all frictionless surfaces and the inclined surface making 37° with horizontal. A block X with mass 2 kg is placed at the highest point of the wedge as shown in figure is at rest. At t=0 wedge (Y) is pulled toward right with constant force (f) of 24 N. Taking the block X at rest at t=0, the time taken by it to slide down 8.8 m on the slope, while Y is on the move, is s. (take tan (37°) = 3/4 and g = 10 m/s2) [figure]

1. 2
2. 4
3. 2
4. 2 2

The time taken by a block of mass m to slide down from the highest point to the lowest point on a rough inclined plane is 50 % more compared to the time taken by the same block on identical inclined smooth plane. Both inclined planes are at 45° with the horizontal. The coefficient of kinetic friction between the rough inclined surface and block is .

1. 3/4
2. 2/3
3. 5/9
4. 4/9

At t=0, a body of mass 100 g starts moving under the influence of a force (5 i+10 j ) N. After 2 s its position is (2x i+5y j ) m. The ratio x:y is .

1. 1 : 2
2. 2 : 5
3. 5 : 2
4. 5 : 4

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