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11th Physics Monthly Test - 2 ( Work, Energy and Power )

MABS Institution

11th Physics Monthly Test - 2 ( Work, Energy and Power )-Aug 2020

Time : 2.30 Hours

Part - A

Multiple Choice Question - Answer All Question

Consider a drop of rain water having mass 1g falling from a height of 1km. It hits the ground with a speed of 50 ms^-1. Take 'g' constant with a value 10 ms^-2. The work done by the (i) gravitational force and the (ii) resistive force of air is

(i) 1.25 J (ii) -8.25 J
(i) 100 J (ii) 8.75 J
(i) 10 J (ii) -8.75 J
(i) -10 J (ii) -8.25 J

In an explosion, a body breaks up into two pieces of unequal masses. In this:

both parts will have numerically equal momentum
lighter part will have more momentum
heavier part will have more momentum
both parts will have equal kinetic energy

A vertical spring with force constant k is fixed on a table. A.ball of mass m at a height h above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance d. The net work done in the process is

\(mg(h+d)-\frac{1}{2}kd^2\)
\(mg(h-d)-\frac{1}{2}kd^2\)
\(mg(h-d)+\frac{1}{2}kd^2\)
\(mg(h+d)+\frac{1}{2}kd^2\)

A car of mass m starts from rest and accelerates so that the instantaneous power delivered to the car has a constant magnitude P_o The instantaneous velocity of this car is proportional to

t²P₀
\(t^{\frac{1}{2}}\)
\(t^{-\frac{1}{2}}\)
\(\frac{t}{\sqrt m}\)

A shell of mass 200 gm is ejected from a gun of mass 4 kg by an explosion that generates 1.05 kJ of energy. The initial velocity of the shell is

40ms^-1
120ms^-1
100ms^-1
80ms^-1

Two masses of 2 g and 6 g are moving with equal kinetic energy. The ratio of the magnitudes of their Linear momenta is,

1: 2
2: 1
2: 6
1 : 3

Two springs A and B having spring constant K_A and K_B(K_A= 2K_B) are stretched by applying force of equal magnitude. If energy stored in spring A is E_A then energy stored in B will be

2E_A
E_A/4
E_A/2
4E_A

A body of mass 4 m is lying in xy-plane at rest. It suddenly explodes into three pieces. Two pieces each of mass m move perpendicular to each other with equal speed v. The total kinetic energy generated due to explosion is

mv²
\(\frac{3}{2}\)mv²
2mv²
4mv²

If the force and displacement are perpendicular to each other, then the work done is

positive
negative
zero
maximum

A body moving along the y-axis of a coordinate system is subjected to a constant force \(\vec F=(-\vec i+2\vec j+3\vec k)N.\) The work done by the force in moving the body through a distance of 5m along the y-axis is

5 J
2 J
1 J
10 J

Part - B

Generic 2 - Answer All Question

A spring which is initially in un-stretched condition, is first stretched by a length x and again by a further length x. The work done in the first case W₁ is one third of the work done in second case W₂True or false?

Define elastic and inelastic collision.

Water in a bucket tied with rope is whirled around in a vertical circle of radius 0.5 m. Calculate the minimum velocity at the lowest point so that the water does not spill from it in the course of motion. (g= 10 ms^-2)

Define watt.

Can a body have energy without momentum?

Express a unit of electrical energy in terms of joule.

A body is moving along the z-axis of a coordinate system under the effect of a constant force F = Find the work done by the force in moving the body a distance of 2 m along the z-axis.

Part - C

Generic 3 - Answer All Question

How high must a body be lifted to gain an amount of P.E.· equal to the K.E. it has when moving at speed 20 ms^-1. (The value of acceleration due to gravity at a place is 9.8 ms^-2).

To simulate car accidents, auto manufacturers study the collisions of moving cars with mounted springs of different spring constants. Consider a typical simulation with a car of mass 1000 kg moving with a speed 18.0 krnh^-1 on a smooth road and colliding with a horizontally mounted spring of spring constant 6.25 x 10^-3Nm^-1. What is the maximum compression of the spring?

Two objects of masses 2 kg and 4 kg are moving with the same momentum of 20 kg m s-1
(a) Will they have same kinetic energy?
(b) Will they have same speed?

What is mechanical energy? What are its two types?

A weight lifter lifts a mass of 250 kg with a force 5000 N to the height of 5m
(a) What is the work done by the weight lifter?
(b) What is the work done by the gravity?
(c) What is the net work done on the object?

After perfectly inelastic collision between two identical particles moving with same speed in different directions, the speed of the particles become half the initial speed. Find the angle between the two before collision.

A bullet of mass 0.02 kg is moving with a speed of 10 ms^-1. It can penetrate 10 cm of a wooden block, and comes to rest. If the thickness of the target would be 6 cm only, find the K.E. of the bullet when it comes out.

Part - D

Generic 5 - Answer All Question

Deduce the relation between momentum and kinetic energy.

Give the expression for work done if angle between force \(\bar{F}\) and displacement \(\bar{s}\) is e. Also, find the dimensions and SI unit of work.

A body of mass 600 g travels in a straight line with velocity v=a\(x^ \frac{3}{2}\) . a=3\(m^{- \frac{1}{4}}\)s^-1 What is the workdone by the net force during its displacement from x = 0 to x = 3 m?

Find the work done in moving a particle along a vectors \(\vec { s } =(\overset { \wedge }{ i } -2\overset { \wedge }{ j } +3\overset { \wedge }{ k } )\)m if applied force is \(\vec { F } =(2\overset { \wedge }{ i } -3\overset { \wedge }{ j } +4\overset { \wedge }{ k } )\)N.
Derive an expression for the gravitational potential energy of a body of mass 'm' raised to a height 'h' above the earth's surface.

What is meant by positive work, negative work and zero work? Give one example of each.

Find the workdone in moving a particle along a vectors \(\vec { S } =(\overset { \wedge }{ i } +2\overset { \wedge }{ j } +6\overset { \wedge }{ k } )\) m if applied force is \(\vec { F } =(2\overset { \wedge }{ i } +3\overset { \wedge }{ j } +\overset { \wedge }{ 5k } )\) N at an angle 60°.

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