PHYSICS BYTES

Rank Booster Test Series - 02

TOPIC : Unit, Dimension and Errors, Vector, Motion in Straight Line, Motion in a Plane | Experimental Skills - Vernier callipers, Screw Gauge

BEWARE OF NEGATIVE MARKING
1.
A body moving at $2~m/s$ can be stopped over a distance x. If its kinetic energy is doubled, how long will it go befoe coming to rest, if the retarding force remains unchanged?
(1) x
(2) 2x
(3) 4x
(4) 8x
2.
A block weighing 10 N travels down a smooth curved track AB joined to a rough horizontal surface (figure). The rough surface has a friction coefficient of 0.20 with the block. If the block starts slipping on the track from a point 1.0 m above the horizontal surface, the distance it will move on the rough surface is : Curved track to horizontal surface
(1) 5.0 m
(2) 10.0 m
(3) 15.0 m
(4) 20.0 m
3.
The kinetic energy of a particle continuously increases with time. In this situation which of the following statement is correct?
(1) the resultant force on the particle must be parallel to the velocity at all instants.
(2) the resultant force on the particle must be at an angle less than are eqial to $90^{\circ}$ with the velocity all the time
(3) its height above the ground level must continuously decrease
(4) the magnitude of its linear momentum is increasing continuously
4.
The work done on a particle of mass m by a force, $K[\frac{x}{(x^{2}+y^{2})^{3/2}}\hat{i}+\frac{y}{(x^{2}+y^{2})^{3/2}}\hat{j}]$ (K being a constant a appropriate dimensions), when the particle is taken from the point (a, 0) to the point (0, a) along a circular path of radius a about the origin in the x-y plane is:
(1) $\frac{2k\pi}{a}$
(2) $\frac{k\pi}{a}$
(3) $\frac{k\pi}{2a}$
(4) 0
5.
System shown in figure is in equilibrium and at rest. The spring and string are massless. Now the string is cut. The acceleration of mass 2m and m just after the string is cut will be : Mass-spring system
(1) $g/2$ upwards, g downwards
(2) g upwards, $g/2$ downwards
(3) g upwards, 2g downwards
(4) 2g upwards, g downwards
6.
A block starts moving up an inclined plane of inclination $30^{\circ}$ with an initial velocity of $v_{0}$. It comes back to its initial position with velocity $\frac{v_{0}}{2}$. The value of the coefficient of kinetic friction between the block and the inclined plane is close to $\frac{I}{1000}$. The nearest integer to I is:
(1) 346
(2) 246
(3) 546
(4) 146
7.
Two blocks of masses 10 kg and 20 kg are connected by a light spring as shown. A force of 200 N acts on the 20 kg mass as shown. At a certain instant the acceleration of 10 kg mass is $12~ms^{-2}$ towards right direction. Two blocks with spring
(1) At that instant the 20 kg mass has an acceleration of $12~ms^{-2}.$
(2) At that instant the 20 kg mass has an acceleration of $4~ms^{-2}.$
(3) The stretching force in the spring is 100 N.
(4) The collective system moves with a common acceleration of $30~ms^{-2}$ when the extension in the connecting spring is the maximum.
8.
Consider the following statement:
Statement I: The work energy theorem is indipendent of Newton's second law
Statement II: Every force encountered in mechantcs does not have an assoclated potential energy.
(1) Both the statements are true
(2) Both the statements are false
(3) Only Statement I is true
(4) Only Statement I is false
9.
The 50 kg homogeneous smooth sphere rests on the $30^{\circ}$ incline A and bears against the smooth vertical wall B. Calculate the contact forces at A and B. Sphere on incline
(1) $N_{B}=\frac{1000}{\sqrt{3}}N$, $N_{A}=\frac{500}{\sqrt{3}}N$
(2) $N_{A}=\frac{100}{\sqrt{3}}N$, $N_{B}=\frac{50}{\sqrt{3}}N$
(3) $N_{A}=\frac{100}{\sqrt{3}}N$, $N_{B}=\frac{500}{\sqrt{3}}N$
(4) $N_{A}=\frac{1000}{\sqrt{3}}N$, $N_{B}=\frac{50}{\sqrt{3}}N$
10.
In the given figure the pulley is assumed massless and frictionless. If the friction force on the object of mass m is f, then its acceleration in terms of the force F will be equal to Block and pulley system
(1) $(F-f)/m$
(2) $(\frac{F}{2}-f)/m$
(3) $F/2m$
(4) None of these
11.
The force required to just move a body up an inclined plane is double the force required to just prevent it from sliding down. If $\phi$ is the angle of friction and $\theta$ is the angle which the plane makes with horizontal, then
(1) $tan~\phi=2~tan~\theta$
(2) $tan~\phi=3~tan~\theta$
(3) $tan~\phi=tan~\theta$
(4) $tan~\theta=3~tan~\phi$
12.
The magnitude of acceleration of blocks of mass 2 kg and 4 kg are respectively (Pulleys and threads are massless) $(g=10~m/s^{2})$ Atwood machine variant
(1) $a_{1}=5~m/s^{2}, a_{2}=2.5~m/s^{2}$
(2) $a_{1}=a_{2}=0$
(3) $a_{1}=a_{2}=\frac{20}{6}m/s^{2}$
(4) $a_{1}=20~m/s^{2}, a_{2}=5~m/s^{2}$
13.
A particle of mass m attached to the end of string of length l is released from the horizontal position. The particle rotates in a circle about O as shown. When it is vertically below O, the string makes contact with a nail N placed directly below O at a distance h and rotates around it. For the particle to swing completely around the nail in a circle. Pendulum with nail
(1) $h < \frac{3}{5}l$
(2) $h \ge \frac{3}{5}l$
(3) $h \ge \frac{2}{5}l$
(4) $h < \frac{2}{5}l$
14.
A block slips with constant velocity on a plane inclined at an angle $\theta$. The same block is pushed up the plane with an initial velocity v. The distance covered by the block before coming to rest is:
(1) $\frac{v_{0}^{2}}{2g~sin~\theta}$
(2) $\frac{v_{0}^{2}}{4g~sin~\theta}$
(3) $\frac{v_{0}^{2}sin^{2}\theta}{4g}$
(4) $\frac{v_{0}^{2}sin^{2}\theta}{2g}$
15.
In the arrangement shown, the mass m will ascend with an acceleration (Pulley and rope are massless) Mass with pulley and force
(1) zero
(2) g
(3) 2g
(4) $g/2$
16.
A pulley is attached to the ceiling of a lift moving upwards. Two particle are attached to the two ends of a string passing over the pulley. The masses of the particles are in the ratio 2: 1. If the acceleration of the particle is $g/2$ (with respect to lift), then the acceleration of the lift will be :
(1) g
(2) $g/2$
(3) $g/3$
(4) $g/4$
17.
Tension in rope at rigid support is: People climbing rope
(1) 760 N
(2) 1360 N
(3) 1580 N
(4) 1620 N
18.
Mr. A, B and C are trying to put a heavy piston into a cylinder at a mechanical workshop in railway yard. If they apply forces $F_{1}$, $F_{2}$ and $F_{3}$ respectively on ropes then for which set of forces at that instant, they will be able to perform the said job? Three men pulling ropes
(1) $\sqrt{3}F_{1}=F_{2}+2F_{3}$
(2) $2F_{2}=\sqrt{3}F_{1}-\frac{F_{3}}{2}$
(3) $F_{3}=2F_{1}-\sqrt{3}F_{2}$
(4) $2F_{1}=F_{2}+F_{3}$
19.
From Newton's second law of motion, it can be inferred that:
(1) No force is required to move a body uniformly
(2) Accelerated motion is always due to an external force
(3) Inertial mass of a body is equal to force required per unit acceleration in the body
(4) all of these
20.
In accordance with Newton's third law of motion:
(1) Action and reaction never balance each other
(2) For appearance of action and reaction, physical constant is not necessary
(3) This law is applicable whether the bodies are at rest or they are in motion
(4) All of these
21.
A heavy uniform chain lies on horizontal table top. If the coefficient of friction between the chain and the table surface is 0.25, then the maximum fraction of the length of the chain that can hang over one edge of the table is:
(1) 20%
(2) 25%
(3) 35%
(4) 15%
22.
A mass M is placed on a very smooth wedge resting on a surface without friction. Once the mass is released, the acceleration to be given to the wedge so that M remains at rest on it. Mass on smooth wedge
(1) a is applied to the left and $a=g~tan~\theta$
(2) a is applied to the right and $a=g~tan~\theta$
(3) a is applied to the left and $a=g~sin~\theta$
(4) a is applied to the left and $a=g~cos~\theta$
23.
Which of the statements are false:
(1) A horse cannot pull a cart and run in empty space.
(2) Passengers are thrown bacward from their seats when a speeding bus stops suddenly.
(3) It is easier to pull a lawn mower than to pust it.
(4) A cricketer moves his hands backwards while holding a catch.
24.
A body with mass 5 kg is acted upon by a force $\vec{F}=(-3\hat{i}+4\hat{j})N.$ If its initial velocity at $t=0$ is $\vec{u}=(6\hat{i}-12\hat{j})ms^{-1}$ the time at which it will just have a velocity along y-axis is
(1) never
(2) 10 s
(3) 2 s
(4) 15 s
25.
If a body placed at the origin is acted upon by a force $\vec{F}=(\hat{i}+\hat{j}+\sqrt{2}\hat{k}),$ then which of the following statements are correct.
(A) Magnitude of F is $(2+\sqrt{2})$
(B) Magnitude of F is 2
(C) F makes an angle of $45^{\circ}$ with the Z-axis
(D) F makes an angle of $30^{\circ}$ with the Z-axis
Select the correct answer using the codes given below.
(1) A and C
(2) B and C
(3) A and D
(4) B and D
26.
How large must F be in the figure shown to give the 700 g block an acceleration of $30~cm/s^{2}?$ The coefficient of friction between all surfaces is 0.15. Blocks and pulley
(1) 2.18 N
(2) 3.18 N
(3) 4 N
(4) 6 N
27.
At time (t) seconds a particle of mass 3 kg has position vector (r) metres where $\vec{r}=3t\hat{i}-4~cost\hat{j}$ find impulse (e) to the force during time interval $0 \le t \le \pi/2$.
(1) $12\hat{j}N-s$
(2) $9\hat{j}N-s$
(3) $4\hat{j}N-s$
(4) $14\hat{j}N-s$
28.
A cart of mass M has a block of mass m attached to it as shown in figure. The coefficient of friction between the block and the cart is $\mu$. What is the minimum acceleration of the cart so that the block m does not fall: Block on accelerating cart
(1) $\mu g$
(2) $g/\mu$
(3) $\mu/g$
(4) $M\mu g/m$
29.
The blades of a windmill sweep out a circle of area A. If the wind (density $\rho$) flows at a velocity v perpendicular to the circle. What is the mass of the air passing through it in time t?
(1) $m=\rho Avt$
(2) $m=\rho Av^{2}t$
(3) $m=\rho Av$
(4) $m=vAt$
30.
The motion of a particle of mass m is given by $x=0$ for $t < 0$ s, $x(t)=A~sin~4\pi t$ for $0 < t < (1/4)$ s $(A > 0)$, and $x=0$ for $t > (1/4)$ s. Which of the following statements is true?
(1) The force at $t=(1/8)$ s on the particle is $-16\pi^{2}Am.$
(2) The particle is acted upon by an impulse of magnitude $4\pi^{2}Am$ at $t=0$ s and $t=(1/4)$ s.
(3) The particle is not acted upon by any force.
(4) The particle is acted upon by a constant force.
31.
A man squatting on the ground gets straight up and stand. The force of reaction of ground on the man during the process is
(1) constant and equal to mg in magnitude.
(2) constant and greater than mg in magnitude.
(3) variable but always greater than mg.
(4) at first greater than mg, and later becomes equal to mg.
32.
In the given figure potential energy functions in one dimension is ploted with position x. The total energy of the particle is indicated by a cross on the ordinate axis then which of the following is wrong. Potential energy graph
(1) Particle can not be found in region $x < -\frac{b}{2}$ and $x > \frac{b}{2}$
(2) Particle will be in rest at $x=\pm\frac{b}{2}$
(3) The maximum KE of the particle will be in the region $-\frac{a}{2} < x < \frac{a}{2}$
(4) The value of maximum KE is $E+V_{1}$
33.
A bullet of mass 0.01 kg and moving with a velocity of $500~m/s$ strikes a block of mass 2 kg suspended from a 5 meter long string. The centre of gravity of the block rises vertically upwards through a height of 0.1 meter. The velocity of the bullet after emerging out of the block will be
(1) $220~m/s$
(2) $2.2~m/s$
(3) $0.22~m/s$
(4) Zero
34.
A small block of mass m is kept on a rough inclined surface of inclination $\theta$ fixed in an elevator. The elevator goes up with a uniform velocity v an block does not slide on the wedge. The work done by force of friction block in time t will be:
(1) zero
(2) $mgvt~cos^{2}\theta$
(3) $mgvt~sin^{2}\theta$
(4) $mgvt~sin~2\theta$
35.
A uniform chain of mass M and length L is held on a horizontal frictionless table with $(1/n)th$ of its length hanging over the edge of the table. The work done in pulling the chain up on the table is
(1) $\frac{MgL}{n}$
(2) $\frac{MgL}{2n}$
(3) $\frac{MgL}{n^{2}}$
(4) $\frac{MgL}{2n^{2}}$
36.
Two identical balls A and B are released from the positions shown in figure. They collide elastically on horizontal portion MN. The ratio of the heights attained by A and B after collision will be (neglect friction): Two balls colliding on horizontal plane
(1) $1:4$
(2) $2:1$
(3) $4:13$
(4) $2:5$
37.
A juggler throws balls continuously at the rate of three in each second each with a velocity of $10~ms^{-1}$. If the mass of each ball is 0.05 kg his power is
(1) 2 W
(2) 50 W
(3) 0.5 W
(4) 7.5 W
38.
Which of the following statements are correct:
(1) Law of conservation of momentum is applied when net external force on the system is zero.
(2) Work energy theorem is applied when only conservative forces on the acting on the system.
(3) In Newton's third law reaction is caused by action and their is a sum delay between them.
(4) Friction force does not work in all cases.
39.
With what minimum velocity $v_{0}$ (w.r.t. belt) should block be projected from left end A towards end B such that it reaches the other end B of conveyer belt moving with constant velocity v? Friction coefficient between block and belt is $\mu$. Block on conveyor belt
(1) $\sqrt{\mu gL}$
(2) $\sqrt{2\mu gL}$
(3) $\sqrt{3\mu gL}$
(4) $2\sqrt{\mu gL}$
40.
An elastic spring is compressed between two blocks of masses 1 kg and 2 kg resting on a smooth horizontal table as shown. If the spring has 12 J of energy and suddenly released, the velocity with which the larger block of 2 kg moves will be when spring is in natural length Compressed spring between blocks
(1) $2~m/s$
(2) $4~m/s$
(3) $1~m/s$
(4) $8~m/s$
41.
A tank on the roof of a 20 m high building can hold $10~m^{3}$ of water. The tank is to be filled from a pond on the ground in 20 minutes. If the pump has an efficiency of 60%, the input power required is
(1) 1.1 kW
(2) 2.74 kW
(3) 5.48 kW
(4) 7.0 kW
42.
Match the column I to column II :
Column I
A. Newton's First law
B. Newton's second law
C. Newton's third law
D. Linear Momentum
Column II
P. $\vec{F}=m\vec{a}$
Q. law of inertia
R. Action and reaction are equal and opposite
S. $\vec{p}=m\vec{v}$
(1) A-Q, B-P, C-R, D-S
(2) A-S, B-P, C-R, D-Q
(3) A-Q, B-R, C-P, D-S
(4) A-Q, B-S, C-R, D-P
43.
A point size mass 100 gm is rotated in a vertical circle using a cord of length 20 cm. When the string makes an angle $60^{\circ}$ with the vertical, the speed of the mass is $1.5~m/s$ The tangential acceleration of the mass in that position is $(g=9.8~m/s^{2})$
(1) $4.9~ms^{-2}$
(2) $4.9\sqrt{2}ms^{-2}$
(3) $4.9\sqrt{3}ms^{-2}$
(4) $9.8~ms^{-2}$
44.
The length of a simple pendulum is 1 m. The bob is given a velocity $7~ms^{-1}$ in horizontal direction from mean position. During upward motion of bob, if the string breaks when it is horizontal, then the maximum vertical height of ascent of bob from mean position is
(1) 2.5 m
(2) 2 m
(3) 3 m
(4) 3.5 m
45.
In the figure, pendulum bob on left side is pulled a side to a height h from its initial position. After it is released it collides with the right pendulum bob at rest, which is of same mass. After the collision, the two bobs stick together and rise to a height. Pendulums colliding
(1) $\frac{3h}{4}$
(2) $\frac{2h}{3}$
(3) $\frac{h}{2}$
(4) $\frac{h}{4}$
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