Middle of Pyramid - Test # 39

A lighter body and heavier body both are moving with same momentum and applied same retarding force. Their stoping distances are $s_{1} a n d s_{2}$ respectively. Then the correct relation between $s_{1} a n d s_{2}$ -
1. $s_{1} > s_{2}$
2. $s_{1} < s_{2}$
3. $s_{1} = s_{2}$
4. None of these

2. When a $5$ kg plastic box is placed deep inside the water, it accelerates up at a rate of $\dfrac{g}{6}$. How much sand should be put inside the box so that it may accelerate down at the rate of $\dfrac{g}{6}$?

1.	$2~\text{kg}$	2.	$3~\text{kg}$
3.	$4~\text{kg}$	4.	$5~\text{kg}$

In a uniform circular motion, which of the following quantity is not constant
1. Angular momentum
2. Speed
3. Kinetic energy
4. Momentum

A metal ring of mass m and radius R is placed on smooth horizontal table and is set rotating about its own axis in such a way that each part of the ring moves with a speed v. Tension in the ring is:
1. $\frac{m v^{2}}{R}$
2. $\frac{m v^{2}}{2 R}$
3. $\frac{m v^{2}}{2 π R}$
4. None of these

While walking on ice one should take small steps to avoid slipping. This is because smaller steps ensure
1. Larger friction
2. Smaller friction
3. Larger normal force
4. Smaller normal force

A motorcycle is going on an overbridge of radius R. The driver maintains a constant speed. As the motorcycle is ascending on the overbridge, the normal force on it:
1. Increases
2. decreases
3. remains the same
4. fluctuates erratically

Two blocks A and B of masses m & 2m respectively are held at rest such that the spring is in natural length. Find the accelerations of both the blocks just after release.

1. $g \downarrow , g \downarrow$
2. $\frac{g}{3} \downarrow , \frac{g}{3} \uparrow$
3. (0, 0)
4. $g \downarrow , 0$

Five persons A, B, C, D & E are pulling a cart of mass 100 kg on a smooth surface and the cart is moving with acceleration 3 $m / s^{2}$ in east direction. When person 'A' stops pulling, it moves with acceleration 1 $m / s^{2}$ in the west direction. When person 'B' stops pulling, it moves with acceleration 24 $m / s^{2}$ in the north direction. The magnitude of the acceleration of the cart when only A & B pull the cart keeping their directions same as the old directions are:
1. 26 $m / s^{2}$
2. $3 \sqrt{71} m / s^{2}$
3. 25 $m / s^{2}$
4. 30 $m / s^{2}$

A body moves along an uneven surface with constant speed at all points. The normal reaction due to ground on the body is:

1.	maximum at $A$
2.	maximum at $B$
3.	minimum at $C$
4.	the same at $A, B$ and $C$

10.

If no external force acts on the system, then the correct statement is:
1. velocity of the centre of mass changes.
2. momentum of the centre of mass is conserved and constant.
3. position of the centre of mass changes with time.
4. None of these.

11.

Two masses, $m$ and $M$, are connected by a light string passing over a smooth pulley. When mass $m$ moves up by $1.4$ m in $2$ sec, the ratio $\frac{m}{M}$ is:

1.	$\frac{13}{15} $	2.	$\frac{15}{13} $
3.	$\frac{9}{7} $	4.	$\frac{7}{9}$

12.

Two blocks A and B of masses 4 kg and 12 kg are placed on a smooth plane surface. A force F of 16 N is applied on A as shown. The force of contact is :

1. 4 N
2. 8 N
3. 12 N
4. 16 N

13.

The engine of a car produces an acceleration of 4 m/s² in the car. If this car pulls another car of the same mass, what will be the acceleration produced?
1. 8 m/s²
2. 2 m/s²
3. 4 m/s²
4. $\frac{1}{2} m / s^{2}$

14.

A truck and a car are moving with equal velocity. If equal retarding force is applied on each, then on applying the brakes both will stop after certain distance
1. Truck will cover less distance before rest
2. Car will cover less distance before rest
3. Both will cover equal distance
4. None

15.

A constant force acts on a body of mass 0.9 kg at rest for 10s. If the body moves a distance of 250 m, the magnitude of the force is
1. 3 N
2. 3.5 N
3. 4.0 N
4. 4.5 N

16.

Two particles of equal masses are revolving in circular paths of radii r₁ and r₂ respectively with the same speed. The ratio of their centripetal forces is
1. $\frac{r_{2}}{r_{1}}$
2. $\sqrt{\frac{r_{2}}{r_{1}}}$
3. ${(\frac{r_{1}}{r_{2}})}^{2}$
4. ${(\frac{r_{2}}{r_{1}})}^{2}$

17.

If the overbridge is concave instead of being convex, the thrust on the road at the lowest position will be
1. $m g + \frac{m v^{2}}{r}$
2. $m g - \frac{m v^{2}}{r}$
3. $\frac{m^{2} v^{2} g}{r}$
4. $\frac{v^{2} g}{r}$

18.

A particle moves in a circular orbit under the action of a central attractive force inversely proportional to the distance ‘r’. The speed of the particle is
1. Proportional to r²
2. Independent of r
3. Proportional to r
4. Proportional to 1/r

19.

A 500 kg car takes a round turn of radius 50 m with a velocity of 36 km/hr. The centripetal force is
1. 250 N
2. 750 N
3. 1000 N
4. 1200 N

20.

A stone of mass of 16 kg is attached to a string 144 m long and is whirled in a horizontal circle. The maximum tension the string can withstand is 16 Newton. The maximum velocity of revolution that can be given to the stone without breaking it will be-
1. 20 ms^–1
2. 16 ms^–1
3. 14 ms^–1
4. 12 ms^–1

21.

A point mass $m$ is suspended from a light thread of length $l,$ fixed at $O$, and is whirled in a horizontal circle at a constant speed as shown. From your point of view, stationary with respect to the mass, the forces on the mass are:

1.		2.
3.		4.

22.

If a cyclist moving with a speed of 4.9 m/s on a level road can take a sharp circular turn of radius 4 m, then coefficient of friction between the cycle tyres and road is
1. 0.41
2. 0.51
3. 0.61
4. 0.71

23.

A mass is supported on a frictionless horizontal surface. It is attached to a string and rotates about a fixed centre at an angular velocity ω₀. If the length of the string and angular velocity are doubled, the tension in the string which was initially T₀ is now
1. T₀
2. T₀/2
3. 4 T₀
4. 8 T₀

24.

Three identical particles are joined together by a thread as shown in figure. All the three particles are moving in horizontal circles centred at O. If the velocity of the outermost particle is v₀, then the ratio of tensions in the three sections of the string is

1. 3 : 5 : 7
2. 3 : 4 : 5
3. 7 : 11 : 6
4. 3 : 5 : 6

25.

A coin, placed on a rotating turn-table slips, when it is placed at a distance of 9 cm from the centre. If the angular velocity of the turn-table is trippled, it will just slip, if its distance from the centre is
1. 27 cm
2. 9 cm
3. 3 cm
4. 1 cm

26.

A mass of 1 kg is suspended by a string A. Another string C is connected to its lower end (see figure). If a sudden jerk is given to C, then

1. The portion AB of the string will break
2. The portion BC of the string will break
3. None of the strings will break
4. The mass will start rotating

27.

A coin is dropped in a lift. It takes time t₁ to reach the floor when lift is stationary. It takes time t₂ when the lift is moving up with constant acceleration. Then:
1. t₁ > t₂
2. t₂ > t₁
3. t₁ = t₂
4. t₁ >> t₂

28.

If the tension in the cable of 1000 kg elevator is 1000 kg weight, the elevator:
1. is accelerating upwards.
2. is accelerating downwards.
3. may be at rest or accelerating.
4. may be at rest or in uniform motion.

29.

In the above diagram, the acceleration of the car will be:
1. 0.25 m/sec²
2. 2.5 m/sec²
3. 5.0 m/sec²
4. 0.025 m/sec²

30.

A particle of mass 0.3 kg is subjected to a force F = –kx with k = 15 N/m. What will be its initial acceleration if it is released from a point 20 cm away from the origin
1. 5 m/s²
2. 10 m/s²
3. 3 m/s²
4. 15 m/s²

31. Sand is being dropped on a conveyor belt at the rate of $M~\text{kg/s}$. The force necessary to keep the belt moving with a constant velocity of $v~\text{m/s}$ will be:
1. $Mv~\text{N}$
2. $2Mv~\text{N}$
3. $\frac{Mv}{2}~\text{N}$
4. zero

32.

A mass of 1 kg is suspended by a thread. It is (i) lifted up with an acceleration 4.9 m/ $s^{2}$ , (ii) lowered with an acceleration 4.9 m/ $s^{2}$ . The ratio of the tension is:
(1) 3 : 1
(2) 1 : 3
(3) 1 : 2
(4) 2 : 1

33.

A ball of mass 0.25 kg attached to the end of a string of length 1.96 m is moving in a horizontal circle. The string will break if the tension is more than 25 N. What is the maximum speed with which the ball can be moved?
(1) 14 m $s^{- 1}$
(2) 3 m $s^{- 1}$
(3) 3.92 m $s^{- 1}$
(4) 5 m $s^{- 1}$

34.

Two bodies with kinetic energies in the ratio 4 : 1 are moving with equal linear momentum. The ratio of their masses is
(1) 1 : 2
(2) 1 : 1
(3) 4 : 1
(4) 1 : 4

35.

Two masses $M_{1} = 5 k g, M_{2} = 10 k g$ are connected at the ends of an inextensible string passing over a frictionless pulley as show. When masses are released, then acceleration of masses will be:

(1) g
(2) $\frac{g}{2}$
(3) $\frac{g}{3}$
(4) $\frac{g}{4}$

36.

A particle of mass 1 kg is thrown vertically upwards with speed 100 m $s^{- 1}$ . After 5 s it explodes into two parts. One part of mass 400 g comes back with speed 25 m $s^{- 1}$ , what is the speed of other part just after an explosion?
(1) 100 m $s^{- 1}$ upward
(2) 600 m $s^{- 1}$ upward
(3) 100 m $s^{- 1}$ downward
(4) 300 m $s^{- 1}$ upward

37.

A stone is attached to one end of a string and rotated in a vertical circle. If string breaks at the position of maximum tension, it will break at:

(1) A
(2) B
(3) C
(4) D

38.

A player takes 0.1 s in catching a ball of mass 150 g moving with velocity of 20 m $s^{- 1}$ . The force imparted by the ball on the hands of the player is:
(1) 0.3 N
(2) 3 N
(3) 30 N
(4) 300 N

39.

A lift of mass 1000 kg which is moving with an acceleration of 1 m $s^{- 2}$ in the upward direction, then the tension developed in the string which is connected to lift is
(1) 9800 N
(2) 10, 800 N
(3) 11, 000 N
(4) 10, 000 N

40.

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

(1) g $μ$ /v
(2) g/v
(3) v/g
(4) v/(g $μ$ )

41.

Three forces acting on a body are shown in the figure below. To have the resultant force only along the y-direction, the magnitude of the minimum additional force needed is

(1) $\sqrt{3} N$
(2) 0.5 N
(3) 1.5 N
(4) $\frac{\sqrt{3}}{4} N$

42.

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
(1) 13 m $s^{- 1}$ and 14 m $s^{- 1}$
(2) 14 m $s^{- 1}$ and 15 m $s^{- 1}$
(3) 15 m $s^{- 1}$ and 16 m $s^{- 1}$
(4) 16 m $s^{- 1}$ and 17 m $s^{- 1}$

43.

A body of mass M hits normally a rigid wall with velocity v and bounces back with the same velocity. The impulse experienced by the body is
(1) zero
(2) Mv
(3) 1.5 Mv
(4) 2 Mv

44.

The force 'F' acting on a particle of mass 'm' is indicated by the force-time graph shown below. The change in momentum of the particle over the time interval from zero to 8 s is

(1) 24 Ns
(2) 20 Ns
(3) 12 Ns
(4) 6 Ns

45.

Three blocks A, B and C of masses 4, 2 and 1 kg respectively, are in contact on a frictionless surface, as shown. If a force of 14 N is applied onto the 4 kg block, then the contact force between A and B is

(1) 6 N
(2) 8 N
(3) 18 N
(4) 2 N

Fill OMR Sheet*

*If above link doesn't work, please go to test link from where you got the pdf and fill OMR from there

CLICK HERE to get FREE ACCESS for 2 days of ANY NEETprep course

1.	\(2~\text{kg}\)	2.	\(3~\text{kg}\)
3.	\(4~\text{kg}\)	4.	\(5~\text{kg}\)

1.	maximum at \(A\)
2.	maximum at \(B\)
3.	minimum at \(C\)
4.	the same at \(A, B\) and \(C\)

1.	\(\frac{13}{15} \)	2.	\(\frac{15}{13} \)
3.	\(\frac{9}{7} \)	4.	\(\frac{7}{9}\)

Please be patient as the PDF generation may take up to a minute.

Fill OMR Sheet*