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(C) 10.0 ms in southern direction9871128329
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(D) 14.14 ms-1 in south-western direction

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Physics (Unit and Measurements, Motion in Straight Line, Motion on plane , Laws of Motion) (Q1-Q45)

1. Write dimension of a in the relation P=

b−x 2 , where P
at
is power, x is distance and t is time.

(A) MLT 2 (B) M −1 L0 T 2

(C) ML−1 T −2 (D) M −1 ¿−2
2. The unit of Stefan-Boltzmann’s constant σ is 8. Two particles having mass ‘M’ and ‘m’ are moving in a
watt 4 calorie circular path having radius R and r. If their periods are
(A) (B) same, then the ration of angular velocity will be
m× K 4 m2 × K 4 r R
watt joule (A) (B)
(C) (D) R r
m2 × K 4 m2 × K 4 R
3. Zero error belongs to the category of
(A) constant errors (B) personal errors
(C) 1 (D)
√ r
(C) intrumental errors (D) accidental errors 9. Which of the following statements is not true ?
(A) Velocity , acceleration and displacement are
4. ABC is the v – t graph of a body. It shows that vectors
(B) A vector quantity has only magnitude while scaler
has both magnitude and direction
(C) Weight, torque momentum and electric field are
vectore.
(D) Mass, work, energy, moment of inertia are scalers.
(A) at B the force is zero. 10. A bullet is dropped from the same height when another
(B) at B the force acts towards directions of motion. bullet is fired horizontally. They will hit the ground
(C) at B the force acts opposite to direction of motion. (A) simultaneously
(D) infinite force is acting at B. (B) depends on the observer
5. A car starts from rest and moves with constant (C) one after the other
acceleration. The ration of the distance covered in the (D) none of these
nth second to that covered in n seconds is
11. If a
⃗ = b⃗ + c⃗ and their magnitudes are 5, 4 and 3
2 1 2 1 respectively, the angle between a
(A) − (B) + ⃗ and c⃗ is
n2 n n2 n π
2 1 2 1 (A) (B) zero
(C) − (D) + 2
n n2 n n2
6. A moving body is covering the distance directly
(C)
( 35 )
cos-1 (D) cos-1
( 45 )
proportional to the square of the time. The acceleration
of the body is 12. Two blocks A and B of masses 6 kg and 3 kg rest on an
(A) increasing (B) decreasing smooth horizontal surface as shown in the figure. If
(C) zero (D) constant coefficient of friction between A and B is 0.4, the
maximum horizontal force which can make them
7. A scooter going due east at 10 ms-1 turns right through without separation is
an angle of 90° . If the speed of the scooter remains
unchanged in taking this run, the change in the velocity
of the scooter is
(A) 20.0 ms-1 in south western direction
(B) zero
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(A) 72 N (B) 40 N resistance, its velocity V varies with the height h above
(C) 36 N (D) 20 N the ground, as

13. With what minimum acceleration can a fireman slide

2
down a rope while its breaking strength is rd of his
3
weight ?
2 1
(A) g (B) g
3 3
(C) g (D) zero

14. Two masses of 10 kg and 20 kg respectively are 19. A body starts from rest at time t = 0, the acceleration
connected by a massless spring as shown in figure. A time graph is shown in the figure. The maximum
force of 200 N acts on the 20 kg mass. At the instant velocity attained by the body will be
when the 10 kg mass has an acceleration of 12 m/s 2, the
acceleration of the 20 kg mass is

(A) 2 ms-2 (B) 4 ms-2 (A) 110 m/s (B) 55 m/s

(C) 10 ms-2 (D) 20 ms-2 (C) 650 m/s (D) 550 m/s
15. A body of mass ‘m’ is moving such that its position 20. A ball of mass (m) 0.5 kg is attached to the end of a
along x = 4t3/2 + 3t – 2. The instantaneous force acting on string having length (L) 0.5 m. The ball is rotated on a
the body is proportional to horizontal circular path about vertical axis. The
(A) t (B) t3/2 maximum tension that the string can bear is 324 N. The
1 maximum possible value of angular velocity of ball (in
(C) t1/2 (D) radian/s) is
√t
16. Three equal weights A, B and C each of 2 kg are hanging
on a string passing over a fixed pulley which is
frictionless as shown. The tension in the string
connection B and C is
(A) 9 (B) 18
(C) 27 (D) 36

21. A particle moves in the x-Y plane under the influence of

a force such that its linear momentum is ⃗ p(t) =A[i^
cos(kt) – ^j sin(kt)], where A and k are constants. The
(A) zero (B) 13 N
angle between the force and the momentum is
(C) 3.3 N (D) 19.6 N
(A) 0° (B) 30°
17. Two masses 40 kg and 30 kg are connected by a
weightless string passing over a frictionless pulley as
(C) 45 ° (D) 90°
shown in the figure. The tension in the string will be
22. A block of mass √ 3 kg is resting on a horizontal plane
(coefficient of static friction μ = 1/2 √ 3). A force ⃗
F is
applied to the block as shown in the figure. The
minimum magnitude of ⃗ F for which the block begins to
slide is (g = 10 m/s2)
(A) 188 N (B) 368 N
(C) 288 N (D) 168 N

18. A ball is dropped vertically from a height d above the

ground. It hits the ground and bounces up vertically to a
height d/2. Neglecting subsequent motion & air (A) 20 N (B) 5N
(C) (20/3) N (D) 10 N
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23. A block of mass 0.1 kg is held against a wall by applying (C) 8:1 (D) 16 : 1
a horizontal force of 5N on the block. If the coefficient of
friction between the block and the wall is 0.5, the 31. With what minimum speed a particle be projected from
magnitude of the frictional force acting on the block is the origin so that it is able to pass through a given point
(A) 2.5 N (B) 0.98 N (30 m, 40 m) ?
(C) 4.9 N (D) 0.49 N (A) 30 ms-1 (B) 40 ms-1
(C) 50 ms -1
(D) 60 ms-1
24. When a spring is loaded with 5 N, its length is α and
32. The velocity of a projectile at the initial point A is u
⃗ = (2i^
when loaded with 4 N, its length is β . When loaded with
9 N, its length would be 7 + 3 ^j ) m/s. It’s velocity (in m/s) at point B is :
(A) 5 α - 4 β (B) α+β
(C) 4 α – 5 β (D) 5α +4 β

25. A+ ⃗
If A = B, what is the angle between (⃗ B) and (⃗
A–⃗
B
)?
(A) 30° (B) 60° (A) 2i^ + 3 ^j (B) -2i^ – 3 ^j
(C) ° (D) °
90 180 (C) -2i^ + 3 ^j (D) 2i^ – 3 ^j

26. If the difference of two unit vectors is a unit vector, then 33. The speed of a projectile is increased by 5% without
the magnitude of their sum is: changing the angle of projection. The percentage
(A) 1/ 2 √ (B) √ 2 increase in the range will be :
(A) 2.5 % (B) 5%
(C) 1/ √3 (D) √3 (C) 7.5 % (D) 10 %
27. The period of a body under S.H.M. is represented by : T
34. An object is kept on a smooth inclined plane of 1 in l.
= PaDbSc, where P is pressure, D is density and S is
The horizontal acceleration to be imparted to the
surface tension. The values of a, b and C are
inclined plane so that the object is stationary relative to
3 1 the incline is
(A) - , ,1 (B) -1 , - 2, 3
2 2 (A) g l 2−1
√ (B) g(l 2−1)
1 3 1 g g
(C) ,- ,- (D) 1, 2, 1/3
2 2 2 (C) 2
(D) 2
√l −1 l −1
28. Acceleration-velocity graph of a 3.25 particle moving in
a straight line is as shown in figure. The slop of velocity- 35. A body takes time t to reach the bottom of an inclined
displacement graph, plane is made rough, time taken is 2 t. The coefficient of
friction is
2 3
(A) tanθ (B) tan θ
3 4
3 1
(C) tanθ (D) tan θ
(A) increases linearly (B) decreases linearly 5 2
(C) is constant (D) increases parabolically
36. Water from a hose pipe of area of cross section A is
29. Two particles are projected simultaneously in the same emerging out with a velocity v and strikes a block of
vertical plane, from the same point, both with different mass m. Find the acceleration produced in the block.
speeds and at different angles with horizontal. The path Density of water is ρ .
followed by one, as seen by the other, is :
(A)
ρAv
(B)
ρA v 2
(A) a vertical line
(B) a parabola m m
(C) a hyperbola ρA
(D) a straight line making a constant angle (90° )
(C) ρAv (D)
v
with the horizontal
37. A particle of mass 4 m which is at rest explodes into
30. Ratio of minimum kinetic energies of two projectiles of three fragments. Two of the fragments each of mass m
same mass is 4 : 1. The ratio of the maximum height are found to move with a speed v each in mutually
attained by them is also 4 : 1. The ratio of their ranges perpendicular directions. The total energy released in
would be : process of explosion is
(A) 2 : 1 (B) 4:1 (A) 2 m v 2 (B) (3/2)m v 2
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(C) m v2 (D) 3m v 2

38. The time period of a simple pendulum of length l

measured in an elevator in an elevator descending with
acc. = g/3 is
3l l
(A) 2 π
2g
2l
√ (B) 2
g
π
3l
√
(C) 2π
3g √ (D) 2π
4g √
3 2
39. The equation of the motion of a projectile is y= 2x - x
4
The horizontal component of velocity is 3 ms -1. What is
the range of projectile ? Given g = 10 ms-2
(A) 1.8 m (B) 3.6 m
(C) 2.7 m (D) 4.5 m

40. If the time of flight of a projectile is doubled, the

maximum height attained will be :
(A) unchanged (B) halved
(C) doubled (D) four times

41. A projectile has initially the same horizontal velocity as

it would acquire if it had moved from rest with uniform
acceleration of 3 ms-2 for 0.5 minutes. If the maximum
height reached by it is 80 m, then the angle of projection
is : (g = 10 ms-2)
(A) tan-1 (3) (B) tan1 (3/2)
(C) tan (4/9)
-1
(D) cot-1 (4/9)

42. If A and B denote the sides of a parallogram and its area

1
is AB (A and B are the magnitude of A
⃗ and B
⃗
2
respectively), the angle between A and B is :
(A) 30° (B) 60°
(C) 45 ° (D) 120°
43. A body freely falling from rest has a velocity v after it
falls through a height h. The distance it has to fall down
further for its velocity to become double is :
(A) h (B) 2h
(C) 3 h (D) 4h

44. A body is thrown vertically upward in air when air

resistance is taken into account, the time of ascent is t 1
and time of descent is t2, then which of the following is
true ?
(A) t1 = t2 (B) t1 < t2
(C) t1> t2 (D) t1≤ t2

45. If 50 m is the distance at which a car can be stopped

when initially it was moving with speed 10 ms-1, then on
making the speed of the car 50 ms-1, the distance at
which the car can be stopped is :
(A) 250 m (B) 500 m
(C) 1000 m (D) 1250