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*Answer can only contain numeric values

QUESTION: 1

Block ** A** is hanging from a vertical spring and it at rest. Block

Solution:

The initial extension in spring is

Just after collision of ** B** with

For the spring to just attain natural length of combined mass must rise up by (see figure.) and comes to rest.

Applying conservation of energy between initial and final states

Alternate solution by SHM

The correct answer is: 6

*Answer can only contain numeric values

QUESTION: 2

In the figure shown a small block ** B** of mass

Solution:

Let ** u** and

** mu** =

Applying conservation of energy between initial and final state as shown in figure (1), we get

solving (1) and (2) we get

...(3)

At the instant block * B* reaches maximum height

Applying conservation of momentum in horizontal direction, we get

Applying conservation of energy between initial and final state

Solving equations (3), (4) and (5) we get

The correct answer is: 25

*Answer can only contain numeric values

QUESTION: 3

Each of the block shown in figure has mass 1 ** kg**. The near block moves with a speed of 2

Solution:

Maximum compression will take place when the blocks move with equal velocity. As no net external horizontal force acts on the system of the two blocks, the total linear momentum will remain constant. If ** v** is the common speed at maximum compression, we have,

(1 * kg*) (2

or ** v** = 1

Initial kinetic energy

Final kinetic energy =

or * x* = 0.2

The correct answer is: 20

*Answer can only contain numeric values

QUESTION: 4

A stationary body explodes into four identical fragments such that three of them fly off mutually perpendicular to each other, each with same kinetic energy., **E**_{0}. The energy of explosion is given by *nE*_{0}. Find the value of **n****.**

Solution:

Let the three mutually perpendicular direction be along ** x**,

By linear momentum conservation,

= 3*E*_{0} + 3**E**_{0}

= 6**E**_{0}

The correct answer is: 6

*Answer can only contain numeric values

QUESTION: 5

A balloon having mass ** m** is filled with gas and is held in hands of a boy. Then suddenly it get released and gas start coming out of it with a constant rate. The velocities of the ejected gases is also constant 2

Solution:

Neglecting gravity

** u** = ejection velocity w.r.t. balloon

The correct answer is: 1.386

*Answer can only contain numeric values

QUESTION: 6

Particle ** A** moves with speed 10

Solution:

For first collision ** v **= 10

velocity of separation = ** e** velocity of approach

**v**_{2} – **v**_{1} = 5**m/s**

for second collision

The correct answer is: 2.5

*Answer can only contain numeric values

QUESTION: 7

A plate of mass ** M** is moved with constant velocity

Solution:

Force ** F** on plate = force exerted by dust particles

= force on dust particles by the plate

= rate of change of momentum of dust particles

= mass of dust particles striking the plate per unit time × change in velocity of dust particles

The correct answer is: 2

*Answer can only contain numeric values

QUESTION: 8

Three ball ** A**,

Solution:

For 1^{st} collision

Since

* e* = 1

⇒

By momentum conservation :

For second collision :

By momentum conservation :

From (2) and (4) :

Therefore ** B** can not collide with

Hence; total number of collision is 2.

The correct answer is: 2

*Answer can only contain numeric values

QUESTION: 9

A particle moving on a smooth horizontal surface strikes a stationary wall. The angle of strikes is equal to the angle of rebound and is equal to 37° and the coefficient of restitution with wall is e = 1/5. Find the friction coefficient between wall and the particle in the form X/10. What is the value of X.

Solution:

Since e = 1/5

∴ Final normal component of velocity

As the angle of rebound is equal to the angle before impact.

Therefore, both normal and tangential components of velocities must change by the same factor,

∴ Tangential velocity after impact becomes

Let the time of impact be Δt.

where ** N** is the normal force imparted on the ball by the wall.

The correct answer is: 5

*Answer can only contain numeric values

QUESTION: 10

Three blocks are placed on smooth horizontal surface and lie on same horizontal straight line. Block 1 and block 3 have mass * m* each and block 2 has mass

Solution:

Let **v**_{1}, **v**_{2} and **v**_{3} be velocities of block 1, 2 and 3 after suffering collision each.

* mv* =

and

The correct answer is: 4.236

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