# Free Objective Test 01 Practice Test - 11th and 12th

A force F=K(yi+aj) (where K is a positive constant) acts on a particle moving in the xy-plane. Starting from the origin, the particle is taken along the positive x-axis to the point (a, 0) and then parallel to the y-axis to the point (a, a). The total work done by the force F on the particles is

A.

2Ka2

B.

2Ka2

C.

Ka2

D.

Ka2

#### SOLUTION

Solution : C

While moving from (0,0) to (a,0)

Along positive x-axis, y = 0 F=kx^j

i.e. force is in negative y-direction while displacement is in positive x-direction.

W1=0

Because force is perpendicular to displacement

Then particle moves from (a,0) to (a,a) along a line parallel to y-axis (x = +a) during this F=k(y^i+a^j)

The first component of force, ky^i will not contribute any work because this components is along negative x-direction (^i) while displacement is in positive y-direction (a,0) to (a,a).

The second component of force i.e. ka^j

W2=(ka^j)(a^j)=(ka)(a)=ka2

So net work done on the particle W=W1+W2

=0+(ka2)=ka2

Which of the following is a scalar quantity

A.

Displacement

B.

Electric field

C.

Acceleration

D.

Work

#### SOLUTION

Solution : D

Work is a dot product of force and displacement and hence a scalar.

If the unit of force and length each be increased by four times, then the unit of energy is increased by

A.

16 times

B.

8 times

C.

2 times

D.

4 times

#### SOLUTION

Solution : A

Work = Force × Displacement

If unit of force and length be increased by four times then the unit of energy will increase by 16 times.

A man pushes a wall and fails to displace it. He does

A.

Negative work

B.

Positive but not maximum work

C.

No work at all

D.

Maximum work

#### SOLUTION

Solution : C

No displacement is there. Hence work is zero.

When work is done on a body by an external force, its

A.

Only kinetic energy increases

B.

Only potential energy increases

C.

Both kinetic and potential energies may increase

D.

Sum of kinetic and potential energies remains constant

#### SOLUTION

Solution : C

Work done will convert into energies - both Kinetic and Potential

The work done in pulling up a block of wood weighing 2 kN for a length of 10m on a smooth plane inclined at an angle of 15 with the horizontal is

A.

4.36 kJ

B.

5.17 kJ

C.

8.91 kJ

D.

9.82 kJ

#### SOLUTION

Solution : B

W=mg sinθ×s

=2×103×sin15×10

=5.17kJ A force acts on a 30 gm particle in such a way that the position of the particle as a function of time is given by x=3t4t2+t3, where x is in metres and t is in seconds. The work done during the first 4 seconds is

A.

5.28 J

B.

450 mJ

C.

490 mJ

D.

530 mJ

#### SOLUTION

Solution : A

v=dxdt=38t+3t2

v0=3m/s and v4=19m/s

W=12m(v24v20)  (According to work energy theorem)

=12×0.03×(19232)=5.28 J

A body moves a distance of 10 m along a straight line under the action of a force of 5 N. If the work done is 25 joule, the angle which the force makes with the direction of motion of the body is

A.

0

B.

30

C.

60

D.

90

#### SOLUTION

Solution : C

W=Fscos θ
cos θ=WFs=2550=12
θ=cos1(12)
θ=60

A body of mass m is moving in a circle of radius r with a constant speed v. The force on the body is mv2r and is directed towards the centre. What is the work done by this force in moving the body over half the circumference of the circle

A.

mv2πr2

B.

Zero

C.

mv2r2

D.

πr2mv2

#### SOLUTION

Solution : B

Work done by centripetal force is always zero, because force and instantaneous displacement are always perpendicular.

W=F.s=Fs cos θ=Fs cos 90=0

Given |A+B|=|AB| Find the angle between A and B

A.

00

B.

450

C.

900

D.

600

#### SOLUTION

Solution : C

A2+B2+2ABcosθ=A2+B22Acosθ4ABcosθ=0cosθ=0θ=90

A moving body of mass m and velocity 3 km/h collides with a body at rest of mass 2m and sticks to it. Now the combined mass starts to move. What will be the combined velocity

A.

3 km/h

B.

2 km/h

C.

1 km/h

D.

4 km/h

#### SOLUTION

Solution : C Initial momentum = m×3+2m×0=3m

Final momentum = 3m×V

By the law of conservation of momentum

3m=3m×VV=1km/h

The kinetic energy acquired by a mass m in travelling a certain distance d, starting from rest, under the action of a force F such that the force F is directly proportional to t is

A.

Directly proportional to t2

B.

Independent of t

C.

Directly proportional to t4

D.

Directly proportional to t

#### SOLUTION

Solution : C

f = kt

mv0 dv = kt0 tdt
mv = kt2
v = kmt2
KE = 12mv2=12mk2m2t4 = (k22m )t4
KE α t4

The blocks A and B shown in fig. Have masses MA=5kg and MB=4kg. The system is released from rest. The speed of B after A has travelled a distance 1 m along the incline is A.

32g

B.

34g

C.

g23

D.

g2

#### SOLUTION

Solution : C

If A moves down the incline by 1 m, B shal move up by 12m.

If the speed of B is v, then the speed of A will be 2v.

From conservation of energy,

Gain in KE = loss in PE

12mA(2v)2+12mBv2=mAg×35mBg×12

Solving, we get

v=g23

The velocity - time graph of a particle moving in a straight line is shown in figure. The mass of the particle is 2kg.Work done by all the forces acting on the particle in time interval between t = 0 to t = 10 s is A.

300 J

B.

−300 J

C.

400 J

D.

−400 J

#### SOLUTION

Solution : A

From work - energy theorem,

W = KE=KfKi=12m(vf2vi2)

=12×2[(20)2(10)2]=300J

The kinetic energy acquired by a mass m in travelling a certain distance d starting from rest under the action of a constant force is directly proportional to

A.

m

B.

Independent of m

C.

1m

D.

m

#### SOLUTION

Solution : B

Kinetic energy acquired by the body

= Force applied on it × Distance covered by the body

K.E=F×d

If F and d both are same then K.E. acquired by the body will be same