CLASS XI PHYSICS DPP 1
CLASS XI - PHYSICS
✤ General instructions:
(1) There are 33 questions in all. All questions are compulsory.
(2) This question paper has five sections: Section A, Section B, Section C,
Section D and Section E.
(3) All the sections are compulsory.
(4) Section A contains sixteen questions, twelve MCQ and four Assertion
Reasoning based of 1 mark each, Section B contains five questions of Two
marks each, Section C contains seven questions of three marks each, Section D
contains two case study-based questions of four marks each and Section E
contains three long answer questions of five marks each.
(5) There is no overall choice. However, an internal choice has been provided in
one question in Section B, one questions in Section C, one question in each
CBQ in Section D and all three questions in Section E: You have to attempt
only one of the choices in such questions.
(6) Use of calculators is not allowed.
✤ SECTION A
1) Which of the following physical quantities is dimensionless?
a) Gravitational constant b) Relative density
c) Surface tension d) Angular momentum
2) A car starts from rest and moves with constant acceleration. Which of
the following graphs is a straight line?
a) Displacement vs. time b) Velocity vs. time
c) Acceleration vs. time d) Both b and c
3) Which of the following statements is true?
a) Speed is always greater than velocity
b) Speed is always equal to velocity
c) Speed is always less than velocity
d) Speed may be greater or equal to velocity
4) The resultant of two vectors of equal magnitude is minimum when the angle between them is:
a) 0° b) 90° c) 180° d) 120°
5) The direction of instantaneous velocity is shown by
(d) none of these 6
6) Identify the correct statement:
a) Static friction depends on the area of contact.
b) Kinetic friction depends on the area of contact.
c) Coefficient of kinetic friction doesn't depend on the nature of the
surfaces in contact.
d) Coefficient of kinetic friction is less than the coefficient of limiting
friction.
7) A ball is travelling with uniform translational motion. This means that
a) it is at rest
b) the path can be straight line or circular and the ball travel with
uniform speed
c) all parts of the ball have the same velocity and the velocity is
constant
d) the centre of the ball moves with constant velocity and the ball
spins about its centre uniformly
8) A force F= 5i +6j -4k acting on a body produces a displacement
s= 6i +5k. The work done by the force is
a) 15 units b)10 units c) 18 units d) 12 units
9) Two bodies of masses m₁ and m₂ have same momentum. The ratio of
their KE is
a) √ m2/m₁ b) √m1/m2
c) m1/m2 d) m2/m1
10) When a disc rotates with uniform angular velocity, which of the
following is not true?
a) The sense of rotation remains same.
b) The orientation of the axis of rotation remains same.
c) The speed of rotation is non-zero and remains same.
d) The angular momentum is zero and remains same.
11) The moment of inertia of a body doesn't depend upon:
a) Angular velocity b) Axis of rotation
c) Mass of a body d) distribution of mass
12) Kepler's second law is based upon:
a) Newton's first law
b) Newton second law
c) Special theory of relativity
d) Conservation of angular momentum
ASSERTION REASON
Choose the correct option in give assertion and reason.
a) Both assertion and reason are true and the reason is the correct
explanation of the assertion.
b) Both assertion and reason are true but reason is not the correct
explanation of the assertion.
c) Assertion is true but reason is false.
d) Assertion is false and reason is also false
e) Assertion is false but reason is true.
13) Assertion: Action and reaction forces don't cancel out each other.
Reason: It is because both do not act on the same body.
14) Assertion: When a body moves along a circular path no work is done
by the centripetal force.
Reason: The centripetal force acts tangentially.
15) Assertion: A force applied at the center of mass of a rigid body
produces only linear acceleration but no angular
acceleration.
Reason: Torque about the center of mass is zero if the line of action
of force passes through it.
16) Assertion: Weight of an object decreases as it is taken deep inside
the Earth.
Reason: Inside the Earth, effective gravitational force varies
linearly with distance from the center.
✤ SECTION B
17) A book with many printing errors contains two different formulae for
a displacement 'y' of a particle undergoing a certain periodic motion
(i) y=a sin (2πt/T) (ii) y=(a/T) sin (t/a); where a= maximum
displacement of the particle, T= time period of motion. Rule out wrong
formulae on dimensional grounds.
18) The length, breadth and height of a rectangular block of wood were
measured to be l=12.13±0.02 cm, b=8.16 ±0.01cm and
h= 3.46±0.01 cm. Determine the percentage error in the volume of the
block.
19) The velocity time graph of a particle moving along a fixed direction is
as shown in figure. Find the displacement in 0s to 10s.
20) (a) If unit vectors å and ĉ are inclined at an angle θ, then prove that
|â – ĉ|= √2 (1-cosθ) 1/2
(b) Can we call the motion of the particle as one with uniform
acceleration? Why?
21) Derive the Expression showing relation between torque and angular
momentum.
✤ SECTION C
22) The time of oscillation T of a small drop of a liquid under surface
tension, whose dimension are those of force per unit length, depends
upon the density d, the radius r and the surface tension σ. Derive
formula for T in terms of d, r and o using dimensional analysis.
23) The displacement x of a particle varies with time t as
X = 34t2-15 t +25.
(i) Find the velocity and acceleration of the particle at t= 0.
24) Obtain all three equations of motion for constant acceleration using
method of calculus or graphical method,
(i) v=u + at (i)s=ut +(1/2)at²
(iii) v²-u²=2as
All symbols are having their usual meanings.
25) Show that the magnitude of resultant of two vectors A and B inclined
at an angle θ is R = (A2+ B² +2ABcosθ)12. Find the direction of
resultant also.
26) (a) Define impulse. Write its SI unit. Derive the expression for an
impulse-momentum theorem.
OR
(b) State and explain the law of conservation of linear momentum with
an example and prove it from Newton's second law of motion.
27) Three masses 3 kg, 4 kg, 5 kg are located at the corners of an equilateral
triangle of side 1 m, then what are the coordinates of the center of mass
of this system.
OR
(b)Prove that | â – ĉ | ≤ | â |+|ĉ |
28) Derive an expression for acceleration due to gravity below the surface
of earth. Show the graphical representation of 'g' with distance from
the center of earth.
✤ SECTION D(Case Study-Based)
29) The turning effect of force is called moment of force or torque. It is measured as the product of the magnitude of the force and the
perpendicular distance between the line of action of force and the axis
of rotation.
t = F X ON =F X d = Fr sinθ
In vector form, τ = r x F
The direction of torque is perpendicular to the plane of r and F and its
sense is given by right hand rule. If a torque applied on a body rotates
it through an angle Δθ, the work done by the torque is
ΔW = τ Δθ = Torque x Angular displacement
Power of torque, P = ΔW/Δt= τ Δθ/Δt = τω
(i) Turning effect of force is produced by
a) Perpendicular component of force
b) Radial component of force
c) None of these
d) both a and b
(ii) Which of the following statement is incorrect?
a) Moment of couple is independent of point about which
moment is taken.
b) For translational equilibrium of a body vector sum of all the
forces on it must be zero
c) A body may be in translational equilibrium but may not be
in rotational equilibrium simultaneously
d) Rotational equilibrium depends on location of origin about
which torques are taken
(iii) If the earth were to shrink suddenly, what would happen to the
length of the day?
a) It increases
b) It remains the same
c) It decreases
d) It becomes unpredictable
(iv) In order to balance a see-saw of total length 10 m, two kids
weighing 20 kg and 40 kg are sitting at an end and at a distance
x from the fulcrum at its centre, respectively. The value x (in cm)
is
a) 250 b) 150 c)450 d) 350
or
(iv) Find the torque of a force F =-3i + j + 5k acting at a point
r= 7 i +3 j + k.(i, j, k are unit vectors along standard axis )
a) 14 i -38 j + 16 k
b) 4 i +4 j + 6 k
c) -14 i +38 j - 16 k
d) -21 i +3 j + 5 k
30) When a spring is stretched through distance x, the restoring force F set
up in the spring due to its elasticity is such that
F ∝ -x or F=-kx where k is a force constant or spring constant of the
spring. It is the restoring force set up in the spring per unit extension.
Its SI unit is N/m. The work done in stretched spring through the
distance x will be
W = 0∫x kxdx = ½kx²
This work done is stored as potential energy U of the spring. Therefore,
U=½ kx²
(i) In the equation,
W = 0∫x kxdx = ½kx²
Write the dimension of k.
(ii) A spring of force constant 800 N/m has an extension of 5 cm. Find
the work done in extending it from 5 cm to 15 cm.
(iii) Two springs of spring constant 1500 N/m and 3000 N/m
respectively are stretched with a same force. Find the ratio of their
potential energies.
(iv) If a spring extends by x on loading, then how much energy will be
stored in the spring in terms of T (where T is the tension in the
spring and k is the spring constant).
OR
(iv) A spring 40 mm long is stretched by the application of a force. If
10 N force is required to stretch the spring through 1mm, then how
much work is done in stretching the spring through 40 mm.
✤ SECTION E
31 I. (a) A projectile is fired with a velocity u making an angle θ with the
horizontal. Obtain the expressions for its
(i) Time of flight (ii) Maximum height of a projectile.
(b) A cricket ball is thrown at speed of 20 ms⁻¹ in a direction 30º
above the horizontal, Calculate
(i) the maximum height
(ii) the time taken by the ball to return to the same level.
OR
II. (a) Define centripetal acceleration. Derive an expression for the
centripetal acceleration of an object moving with uniform speed
v along a circular path of radius r.
(b) A stone tied to the end of a string 80 cm long is whirled in a
horizontal circle with the constant speed. If the stone makes 14
revolutions in 25s, what is the magnitude and direction of the
acceleration of the stone?
32 I. (a) Why are circular roads banked? Derive an expression for the
maximum safe speed of a car on a banked circular road having
coefficient of friction μ.
(b) A circular race track of radius 300 m is banked at angle of 15° .If
the coefficient of friction between the wheels of a race car and the
road is 0.2. What is the
(i) Optimum speed of the race car to avoid wear and tear
on its Tyre
(ii) Maximum permissible speed to avoid slipping?
(tan15°=0.267)
II. (a) Define:
(i) Angle of friction
(ii) kinetic friction
(iii) Angle of repose
OR
(b) What is the acceleration of the block and the trolley system
shown in figure. If the coefficient of kinetic friction between the
trolley and the surface is 0.04. What is the tension in the string?
Neglect the mass of the string.
33 I. (a) A body tied to one and of string is made to revolve in a vertical
circle. Draw diagram and use it to find the expression for
(i) The velocity of the body and
(ii) Tension in the string, at lowest and highest point of
the circle.
OR
II. (a)Prove that
(i) In an elastic one-dimensional collision between two
bodies, the relative velocity of approach before
collision is equal to the relative velocity of separation
after collision.
(ii) When two bodies of equal masses suffer one
dimensional elastic collision, their velocities get
exchanged after the collision.
* * * * * * * * * * * * * * *
