Important 1mark -chapter 3,4

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Questions:

Multiple Choice Question

40 x 1 = 40

A block of mass 3kg is at rest on a rough inclined plane with angle of inclination 30° with horizontal. If \(\mu\)s = 0.7, then the frictional force is ____________.

(a)

17.82 N

(b)

1.81 N

(c)

3.63 N

(d)

2.1 N

The ratio of velocities of equal masses in an inelastic collision with one of the masses is stationary is _____________.

(a)

\(\frac { 1-e }{ 1+e } \)

(b)

\(\frac { 1+e }{ e-1 } \)

(c)

(1 + e) (1 - e)

(d)

\(\frac { e-1 }{ e+1 } \)

Which of the following quantity is conserved in all collision process?

(a)

kinetic energy

(b)

linear momentum

(c)

both (a) and (b)

(d)

none.

Three masses is contact as shown. It force F is applied to mass m₁, then the contact force acting on mass m₃ is ________________.

(a)

\(\frac { F }{ { m }_{ 1 }+{ m }_{ 2 }+{ m }_{ 3 } } \)

(b)

\(\frac { { m }_{ 1 }F }{ \left( { m }_{ 1 }+{ m }_{ 2 }+{ m }_{ 3 } \right) } \)

(c)

\(\frac { ({ m }_{ 2 }+{ m }_{ 3 })F }{ \left( { m }_{ 1 }+{ m }_{ 2 }+{ m }_{ 3 } \right) } \)

(d)

\(\frac { { m }_{ 3 }F }{ { m }_{ 1 }+{ m }_{ 2 }+{ m }_{ 3 } } \)

The body must have a minimum speed of lowermost point in vertical circular motion to complete the circle _________________.

(a)

\(\ge \sqrt { gr } \)

(b)

\(\ge \sqrt { 2gr } \)

(c)

\(\ge \sqrt { 5gr } \)

(d)

\(\ge\)5gr

If force is the cause then the effect is ____________.

(a)

mass

(b)

potential energy

(c)

acceleration

(d)

Inertia

The law which is valid in both inertial and non-inertial frame is ____________.

(a)

Newton's first law

(b)

Newton's second law

(c)

Newton's third law

(d)

none

If kinetic energy of a body is increased by 300% then percentage change in momentum will be ___________.

(a)

100%

(b)

150%

(c)

265%

(d)

73.2%.

Two masses as shown in the figure are suspended from a massless pulley. The acceleration of the system when masses are left free is ______________.

(a)

\(\frac { 2g }{ 3 } \)

(b)

\(\frac { g }{ 3 } \)

(c)

\(\frac { g }{ 9 } \)

(d)

\(\frac { g }{ 7 } \)

10.

A roller coaster is designed such that riders experience "weightlessness" as they go round the top of a hill whose radius of curvature is 20 m. The speed of the car at the top of the hill is between ______________.

(a)

16 m/s and 17 m/s

(b)

13 m/s and 14 m/s

(c)

14 m/s and 15 m/s

(d)

15 m/s and 16 m/s

11.

If a body is raised from the surface of the earth upto height R, what is the change in potential energy?

(a)

mgR

(b)

\(\frac{3}{2}mgR\)

(c)

\(\frac{mgR}{2}\)

(d)

\(\frac{mgR}{4}\)

12.

A body is said to be doing a negative work if ______________.

(a)

it does work in the direction of force

(b)

work is done against a force

(c)

work is done by a force

(d)

it does no work

13.

For bodies of same momenta, their velocities are ______________.

(a)

directly proportional to their acceleration

(b)

inversely proportional to their masses

(c)

directly proportional to their masses

(d)

inversely proportional to their forces

14.

An athlete running in a race will continue to run even after reaching the finishing point. It is due to _______________.

(a)

inertia of rest

(b)

inertia of motion

(c)

inertia of direction

(d)

both (b) and (c)

15.

An engine pumps water continuously through a hose. Water leaves the hose with a velocity v and m is the mass per unit length of the water of the jet. What is the rate at which kinetic energy is imparted to water?

(a)

\({{1}\over{2}}{m}{v}^{2}\)

(b)

mv³

(c)

\({{1}\over{2}}{m}{v}^{3}\)

(d)

\({{1}\over{2}}{m}{v}^{2}\)

16.

A block B is pushed momentarily along a horizontal surface with initial velocity v- μ coefficient of friction between B and surface, block B will come to rest after a time ___________.

(a)

v/gμ

(b)

gμ/v

(c)

g/v

(d)

v/g

17.

A force of 2.5 N acts on a body of mass 10 g. What is the acceleration of the body?

(a)

1.5\(\times\)10² ms^-2

(b)

2.0\(\times\)10³ ms^-2

(c)

2.5\(\times\)10³ ms^-2

(d)

3.0\(\times\)10² ms^-2

18.

A machine gun has mass 15 kg. It fires 15 g bullet at the rate of 200 bullets per minutes with a speed of 150 m/s. Then the recoil velocity of the gun is ____________.

(a)

20 ms^-1

(b)

15 ms^-1

(c)

150 ms^-1

(d)

0.2 ms^-1

19.

A body of mass 30 kg climbs on a rope. The boy climbs up with an acceleration of 5 ms^-2What is the tension of a rope?

(a)

250 N

(b)

540 N

(c)

312 N

(d)

444 N

20.

A body of mass 20 kg moving with a uniform velocity of 4 ms^-1. Then the net force acting on a body is _____________.

(a)

constant

(b)

increase

(c)

decrease

(d)

Zero

21.

A marble block of mass 3 kg lying on ice when given a velocity of 5 ms^-1is stopped by friction in 10s. Then the coefficient of friction is ______________.

(a)

0.01

(b)

0.05

(c)

0.03

(d)

0.06

22.

A body is falling from a height h. After it has fallen a height \(\frac{h}{2}\) it will possess _______________

(a)

only Potential Energy

(b)

only Kinetic Energy

(c)

half potential and half kinetic energy

(d)

more kinetic and less potential energy

23.

A force\(\overrightarrow { F } =3\hat { i } +c\hat { j } +2\hat { k } \) acting on a particle causes a displacement \(\overrightarrow { S } =(2\hat { i } -3\hat { j } +4\hat { k } )\) in its own direction. If the work done is 8J, then the value of c is ______________.

(a)

(b)

(c)

(d)

24.

A ball moves on a frictionless inclined table without slipping. The work done by the table surface on the ball is ____________.

(a)

positive

(b)

negative

(c)

zero

(d)

none

25.

A block is kept on a frictionless inclined surface with angle of inclination ∝, The incline is given an acceleration a to keep the block stationary. Then a is equal to _____________.

(a)

g cosec ∝

(b)

(c)

\(\frac { g }{ tan\ \alpha } \)

(d)

g tan ∝

26.

A ball bounces to 75% of its original height. Calculate the mechanical energy lost in each bounce _________________.

(a)

0.40

(b)

0.35

(c)

0.25

(d)

0.20

27.

A particle which is constrained to move along x-axis, is subjected to a force in the same direction which varies with the distance x of the particle from the origin as F(x) = kx + ax³. Here, k and a are positive constants. For x ≥ 0, the functional form of the potential, energy U(x) of the particles

(a)

(b)

(c)

(d)

28.

A particle is placed at the origin and a force F = kx is acting on it (where k is a positive constant). If U (0) = 0, the graph of U(x) versus x will be (where U, is the potential , energy function)

(a)

(b)

(c)

(d)

29.

A wind-powered generator converts wind energy into electric energy. Assume that the generator converts a fixed fraction of the wind energy intercepted by its blades into electrical energy. For wind speed v, the electrical power output will be proportional to

(a)

(b)

v²

(c)

v³

(d)

v⁴

30.

If the potential energy of the particle is \(\alpha -\frac { \beta }{ 2 } { x }^{ 2 }\), then force experienced by the particle is

(a)

F = \(\frac { \beta }{ 2 } { x }^{ 2 }\)

(b)

F = βx

(c)

F = -βx

(d)

F = -\(\frac { \beta }{ 2 } { x }^{ 2 }\)

31.

If the linear momentum of the object is increased by 0.1% then the kinetic energy is Increased by

(a)

0.1 %

(b)

0.2 %

(c)

0.4 %

(d)

0.01 %

32.

What is the minimum velocity with which a body of mass m must enter a vertical loop of radius R so that it can complete the loop?

(a)

\(\sqrt{2gR}\)

(b)

\(\sqrt{3gR}\)

(c)

\(\sqrt{5gR}\)

(d)

\(\sqrt{gR}\)

33.

The potential energy of a system increases, if work is done

(a)

by the system against a conservative force

(b)

by the system against a non-conservative force

(c)

upon the system by a conservative force

(d)

upon the system by a non- conservative force

34.

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

(a)

mv²

(b)

\(\frac{3}{2}\)mv²

(c)

2mv²

(d)

4mv²

35.

A uniform force of (2\(\hat { i }\)+\(\hat { j }\)) N acts on a particle of mass 1 kg. The particle displaces from position (3\(\hat { j }\)+\(\hat { k }\)) m to (5\(\hat { i }\)+3\(\hat { j }\)) m. The work done by the force on the particle is

(a)

9 J

(b)

6 J

(c)

10 J

(d)

12 J

36.

If a person moving from pole to equator, the centrifugal force acting on him

(a)

increases

(b)

decreases

(c)

remains the same

(d)

increases and then decreases

37.

When an object is at rest on the inclined rough surface ____________.

(a)

static and kinetic frictions acting on the object is zero

(b)

static friction is zero but kinetic friction is not zero

(c)

static friction is not zero and kinetic friction is zero

(d)

static and kinetic frictions are not zero

38.

When the object is moving at constant velocity on the rough surface

(a)

net force on the object is zero

(b)

no force acts on the object

(c)

only external force acts on the object

(d)

only kinetic friction acts on the object

39.

A vehicle is moving along the positive x direction, if sudden brake is applied, then

(a)

frictional force acting on the vehicle is along negative x direction

(b)

frictional force acting on the vehicle is along positive x direction

(c)

no frictional force acts on the vehicle

(d)

frictional force acts in downward direction

40.

When a car takes a sudden left turn in the curved road, passengers are pushed towards the right due to

(a)

inertia of direction

(b)

inertia of motion

(c)

inertia of rest

(d)

absence of inertia

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Answers Key:

Multiple Choice Question

40 x 1 = 40

(a)
17.82 N

(a)
\(\frac { 1-e }{ 1+e } \)

(b)
linear momentum

(d)
\(\frac { { m }_{ 3 }F }{ { m }_{ 1 }+{ m }_{ 2 }+{ m }_{ 3 } } \)

(a)
100%

(b)
\(\frac { g }{ 3 } \)

10.

11.

12.

(b)
work is done against a force

13.

(b)
inversely proportional to their masses

14.

(b)
inertia of motion

15.

Mass per unit length = m
Velocity = v
(mass of water pumped in one second)
M = mv
\(\text { Kinetic energy }=\frac{1}{2} M v^{2}\)
\(=\frac{1}{2} m v^{3}\)

16.

(a)
v/gμ

17.

18.

(d)
0.2 ms^-1

19.

(d)
444 N

20.

(d)
Zero

21.

(b)
0.05

22.

23.

24.

25.

(d)
g tan ∝

26.

27.

\(F=-\frac{d u}{d x} \quad F(x) =k x+a x^{3} \)
\(d u =-F d x \)
\(u(x) =-\int_{0}^{x}\left(-k x+a x^{3}\right) d x \)
\(=\int_{0}^{x} k x d x-a \int_{0}^{x} x^{3} d x \)
\(=\frac{k x^{2}}{2}-\frac{a x^{4}}{2} \)
\(U(x) =\frac{x^{2}}{2}\left(k-\frac{a x^{2}}{2}\right) \)
\(u(x)=0 \text { at } x=0 \text { and }\)
\(U(x) =0 ; k-\frac{a x^{2}}{2}=0 \)
\(=\frac{a}{2} x^{2}=-k \)
\(x^{2} =\frac{2 k}{a} \)
\(\therefore x =\sqrt{\frac{2 k}{a}} \)
\(\text { Clearly } u(x)=0 \text { at } x=0 \text { and }\)
\(x=\sqrt{\frac{2 k}{a}}\)
\(\text { For } x>\sqrt{\frac{2 k}{a}} U(x) \text { will be negative. } \)
\(\text { At } x=0 ; F=\frac{-d u}{d x}=0\)
(i.e.,) Slope of V - x graph is zero at x = 0
Hence the most appropriate answer is d.

28.

For a conservative force
\(F=-\frac{d v}{d t} \)
\(\int_{0}^{u(x)} d v=-\int_{0}^{x} F d x=-\int_{0}^{x} k x d x \)
\(\text { As } v(0)=0\)
\(U(x)=-\frac{k x^{2}}{2}\)
Thus, the graph of U(x) versus (x) will be a parabola, symmetric about U - ax is bying below x - ax is with its vertex at the origin. Hence the correct answer is C

29.

\(\text { Force }=v \frac{d m}{d t}\)
\(=v \frac{d}{d t} \text { (volume } \times \text { density) }\)
\(=v \frac{d}{d t}(A x p) \)
\(=v A p \frac{d x}{d t} \)
\(=v \times A p \times v \)
\(=A p v^{2} \)
Power = Force x Velocity
\(=A p v^{2} \times v=A p v^{3}\)
\(\therefore \text { Power } \alpha v^{3}\)

30.

\(\text {Potential energy } P . E=\alpha-\frac{\beta}{2} x^{2}\)
P.E = Work = Fx
\(P=\alpha-\frac{\beta}{2} x^{2}\)
\(\text {Force }=\frac{d p}{d x}=\frac{d}{d x}\left(\alpha-\frac{\beta}{2} x^{2}\right)\)
\(=0-\frac{\beta}{2} \times 2 x =-\beta x \)

31.

\(\text { Kinetic energy } E_{k}=\frac{p^{2}}{2 m}\)
\(\frac{\Delta E_{k}}{E_{k}}=\frac{2 \Delta p}{p}\)
\(\text {Given that } \frac{\Delta p}{p}=0.1\)
∴ Increase in kinetic energy
\(\frac{\Delta E_{k}}{E_{k}}=2 \frac{\Delta p}{p} \)
\(\frac{\Delta E_{k}}{E_{k}}=2 \times 0.1=0.2 \% \)

32.

Radius =R
\(v_{1}^{2}-v_{2}^{2}=4 g R\)
\(\text { Tension } T_{2}=\frac{m v_{2}^{2}}{R_{2}}-m g\)
\(\text {To find minimum speed, let } T_{2}=0\)
\(0 =\frac{m v_{2}^{2}}{R}-m g \)
\(\frac{m v^{2}}{R} =m g \)
\(v_{2}^{2}=R g \ v_{2} =\sqrt{g R} \)
\(\text { sub (2) in the eqn (1) we get }\)
\(v_{1}^{2}-(\sqrt{g R})^{2} =4 g R \)
\(v_{1}^{2}-g R =4 g R \)
\(v_{1}^{2} =4 g R+g R \)
\(=5 g R \)
\(v_{1} =\sqrt{5 g R} \)

33.

(a)
by the system against a conservative force

34.

Using law of conservation of momentum,
\(2 m v =\sqrt{m^{2} v^{2}+m^{2} v^{2}} \)
\(=\sqrt{2 m^{2} v^{2}} \)
\(v =\frac{\sqrt{2} m v}{2 m}=\frac{v}{\sqrt{2}} \)
Energy released in explosion = \(2 \times \frac{1}{2} m v^{2} +\frac{1}{2} \times 2 m \times\left(\frac{v^{2}}{\sqrt{2}}\right)^{2} \)
\(=m v^{2}+m \times \frac{v^{2}}{2} \)
\(=\frac{3}{2} m v^{2} \)

35.

\(\text { Force } \overrightarrow{\mathbf{F}}=(2 i+\vec{j}) N\)
\(\text { Displacement } d=(5 \vec{i}+3 \vec{j})-(3 \vec{j}+\vec{k})\)
\(=(5 i-k) m\)
\(\text { Work done } W=F . d\)
\(=(2 \vec{i}+\vec{j})(5 i-k)\)
\(=10-0-0=10 J \)

36.