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*Answer can only contain numeric values

QUESTION: 1

In the figure shown initially spring is in unstretched state and blocks are at rest. Now 100*N* force is applied on block * A* and

Solution:

The correct answer is: -6

*Answer can only contain numeric values

QUESTION: 2

Starting at rest, a 5*kg* object is acted upon by only one force as indicated in the figure. Find the total work done (in *Joule*) by the force on the object :

Solution:

The correct answer is: 90

*Answer can only contain numeric values

QUESTION: 3

A particle is projected vertically upwards with a speed of 16*m/s*, after some time, when it again passes through the point of projection, its speed is found to be 8*m/s*. It is known that the work done by air resistance is same during upward and downward motion. Then the maximum height (in *m*) attained by the particle is : (Take * g* = 10

Solution:

From work energy theorem for upward motion

(work by air resistance) for downward motion

or *h* = 8*m*

The correct answer is: 8

*Answer can only contain numeric values

QUESTION: 4

A particle * A* of mass 10/7 kg is moving in the positive

(use the graph given)

Solution:

Area under *P*-*x* graph

From graph;

The correct answer is: 4

*Answer can only contain numeric values

QUESTION: 5

The blocks of mass **m**_{1} = 1*kg* and ** m_{2}** = 2

Solution:

For the block of mass **m**_{2}, not to move, the maximum compression in the spring ** x_{0}** should be such that

kx_{0} = μm_{2 } .....(i)

Applying work energy theorem to block of mass *m*_{1} we get

From equation (1) and (2) we get

putting the appropriate value we get μ = 10m/s.

The correct answer is: 10

*Answer can only contain numeric values

QUESTION: 6

A block of mass * m* is attached with a massless spring of force constant

(neglect mass of string and pulley and friction in pulley.)

Solution:

As long as the block of mass *m* remains stationary, the block of mass *M* released from rest comes down by (before coming it rest momentarily again).

Thus the maximum extension in spring is

for block of mass *m* to just move up the incline

The correct answer is: 0.6

*Answer can only contain numeric values

QUESTION: 7

In the given figure, the magnitude of work done by frictional force on upper and lower block?

Solution:

Assume 20*kg* and 30*kg* block move together

∴ friction force on 20*kg* block is * f* = 20 × 1 = 20

The maximum value of frictional force is

Hence no slipping is occurring.

∴ The value of frictional force is * f* = 20

Distance traveled in ** t **= 2 seconds.

Work done by frictional force on upper block is

**W _{friction}** = 20 × 2 = 40

Work done by friction force on lower block is = –20 × 2 = –40

The correct answer is: 40

*Answer can only contain numeric values

QUESTION: 8

A fire hose has a diameter of 2.5*cm* and is required to direct a jet of water to a height of at least 40*m*. The minimum power (in *kW*) of the pump needed for this hose is :

Solution:

The speed of the water leaving the hose must be if it is to reach a height * h* when directed vertically upward. If the diameter is

⇒ Mass ejected is

This kinetic energy of this water leaving the hose

The correct answer is: 2.15

*Answer can only contain numeric values

QUESTION: 9

If there is no friction any where, the speed of the wedge, as the block leaves the wedge is :

Solution:

Linear momentum is conserved only in horizontal direction.

mv_{1}=mv_{2}…..(i)

1/2(mv_{1})^{2}+1/2(mv_{2})^{2 }= mgh....(ii)

From (i)&(ii),

v_{2}= 10ms^{-1}

*Answer can only contain numeric values

QUESTION: 10

A spring lies along an x-axis attached to a wall at one end and a block at the other end. The block rests on a frictionless surface at ** x** = 0. A force of constant magnitude

During the displacement, which of the curves shown in the graph best represents the kinetic energy of the block.

Solution:

Applying *W*-*E* theorem on the block for any compression * x* :

⇒ * KE* vs

The correct answer is: 3

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