Laws of Motion

Three blocks M1, M2, M3 having masses 4 kg, 6 kg and 10 kg respectively are hanging from a smooth pulley using rope 1, 2 and 3 as shown in figure. The tension in the rope 1, T1 when they are moving upward with acceleration of 2 ms-2 is N (if g = 10 m/s2). [figure]

A particle moves in x-y plane under the influence of a force F such that its linear momentum is p(t) = i (kt) - j (kt). If k is constant, the angle between F and p will be :

1. 2
2. 3
3. 4
4. 6

A heavy box of mass 50 kg is moving on a horizontal surface. If co-efficient of kinetic friction between the box and horizontal surface is 0.3 then force of kinetic friction is :

1. 1470 N
2. 147 N
3. 1.47 N
4. 14.7 N

A wooden block, initially at rest on the ground, is pushed by a force which increases linearly with time t. Which of the following curve best describes acceleration of the block with time :

1. [figure]
2. [figure]
3. [figure]
4. [figure]

A 2 kg brick begins to slide over a surface which is inclined at an angle of 45 with respect to horizontal axis. The co-efficient of static friction between their surfaces is:

1. 1
2. 1.7
3. 0.5
4. 1 3

Consider a block and trolley system as shown in figure. If the coefficient of kinetic friction between the trolley and the surface is 0.04, the acceleration of the system in ms-2 is : (Consider that the string is massless and unstretchable and the pulley is also massless and frictionless) : [figure]

1. 1.2
2. 4
3. 3
4. 2

A ball of mass 0.5 kg is attached to a string of length 50 cm. The ball is rotated on a horizontal circular path about its vertical axis. The maximum tension that the string can bear is 400 N. The maximum possible value of angular velocity of the ball in rad/s is :

1. 1600
2. 20
3. 40
4. 1000

A body of mass 4 kg experiences two forces F1=5 i+8 j+7 k and F2=3 i-4 j-3 k. The acceleration acting on the body is :

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

A cricket player catches a ball of mass 120 g moving with 25 m/s speed. If the catching process is completed in 0.1 s then the magnitude of force exerted by the ball on the hand of player will be (in SI unit) :

1. 30
2. 24
3. 12
4. 25

In the given arrangement of a doubly inclined plane two blocks of masses M and m are placed. The blocks are connected by a light string passing over an ideal pulley as shown. The coefficient of friction between the surface of the plane and the blocks is 0.25. The value of m, for which M=10 kg will move down with an acceleration of 2 m/s2, is: (take g=10 m/s2 and 37 =3/4) [figure]

1. 4.5 kg
2. 6.5 kg
3. 9 kg
4. 2.25 kg