Laws of Motion

A circular table is rotating with an angular velocity of rad/s about its axis (see figure). There is a smooth groove along a radial direction on the table. A steel ball is gently placed at a distance of 1 m on the groove. All the surfaces are smooth. If the radius of the table is 3 m, the radial velocity of the ball w.r.t. the table at the time ball leaves the table is x 2 m/s, where the value of x is . [figure]

A light string passing over a smooth light pulley connects two blocks of masses m1 and m2 (where m2 > m1). If the acceleration of the system is g 2, then the ratio of the masses m1m2 is:

1. 1 + 5 5 - 1
2. 3 + 1 2 - 1
3. 2 - 1 2 + 1
4. 1 + 5 2 - 1

A car of 800 kg is taking turn on a banked road of radius 300 m and angle of banking 30 . If coefficient of static friction is 0.2 then the maximum speed with which car can negotiate the turn safely: (g = 10 m/s2, 3 = 1.73 )

1. 51.4 m/s
2. 102.8 m/s
3. 70.4 m/s
4. 264 m/s

A body of weight 200 N is suspended from a tree branch through a chain of mass 10 kg. The branch pulls the chain by a force equal to (if g = 10 m/s2) :

1. 300 N
2. 100 N
3. 150 N
4. 200 N

A wooden block of mass 5 kg rests on a soft horizontal floor. When an iron cylinder of mass 25 kg is placed on the top of the block, the floor yields and the block and the cylinder together go down with an acceleration of 0.1 ms-2. The action force of the system on the floor is equal to :

1. 297 N
2. 291 N
3. 196 N
4. 294 N

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