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QUESTION: 1

A plank is held at an angle α to the horizontal (Figure) on two fixed supports *A* and *B*. The plank can slide against the supports (without friction) because of its weight **Mg**. Find the acceleration and direction in which a man of mass **m** should move so that the plank does not move.

Solution:

F.B.D. of man and plank are

For plank to be a rest, applying Newton's second law to plank along the incline

and applying Newton's second law to man along the incline.

........(2)

down the incline

The correct answer is:

down the incline

QUESTION: 2

A particle of mass 2*kg* moves with an initial velocity of on the *xy-*plane. A force acts on the particle. The initial position of the particle is **(2 m, 3m).** Then for

Solution:

Let at any time, the coordinates be (*x*,*y*).

and

When * y* = 3m,

when

The correct answer is: Possible value of

QUESTION: 3

Mass * m* shown in the figure is in equilibrium. If it is displaced further by

Solution:

Initially the block is at rest under action of force **2 T** upward and mg downwards. When the block is pulled downwards by

∴ acceleration of the block is =

The correct answer is:

QUESTION: 4

A block of mass * m* lies on wedge of mass

Solution:

For no relative motion between wedge and block, let the acceleration of both block and wedge be * a* towards left.

From FBD of block

...(1)

and ......(2)

From FBD of wedge

...(3)

from equation (1), (2) and (3) solving we get

The correct answer is:

QUESTION: 5

In the figure shown the acceleration of *A* is, then the acceleration of *B* is : (*A* remains in contact with *B*)

Solution:

From wedge constraint

The correct answer is:

QUESTION: 6

A cylinder rest in a supporting carriage as shown. The side *AB* of carriage makes an angle 30° with the horizontal and side *BC* is vertical. The carriage lies on a fixed horizontal surface and is being pulled towards left with an horizontal acceleration * a*. The magnitude of normal reactions exerted by sides

Solution:

The force body diagram of cylinder is as shown.

Since net acceleration of cylinder is horizontal.

or ......(1)

and

or ...(2)

Hence *N _{AB}* remains constant and

The correct answer is:

QUESTION: 7

A light spring is compressed and placed horizontally between a vertical fixed wall and a block free to slide over a smooth horizontal table top as shown in the figure. The system is released from rest. The graph which represents the relation between the magnitude of acceleration * a* of the block and the distance

Solution:

Let the initial compression of spring be l. Then the acceleration after the block travels a distance *x* is

⇒ ∴ The graph of a vs *x* is

The correct answer is:

QUESTION: 8

Four identical metal butterflies are hanging from a light string of length **5 l** at equally placed points as shown in the figure. The ends of the string are attached to a horizontal fixed support. The middle section of the string is horizontal. The relation between the angle

Solution:

The correct answer is:

QUESTION: 9

A block is lying on the horizontal frictionless surface. One end of a uniform rope is fixed to the block which is pulled in the horizontal direction by applying a force F at the other end. If the mass of the rope is half the mass of the block, the tension in the middle of the rope will be

Solution:

The acceleration of block-rope system is

where * M* is the mass of block and

So the tension in the middle of the rope will be

Given that

The correct answer is: 5

QUESTION: 10

A pendulum of mass * m* hangs from a support fixed to a trolley. The direction of the string when the trolley rolls up a plane of inclination with acceleration

Solution:

The correct answer is:

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