a body starts from rest with uniform acceleration. if its velocity … · 2020. 8. 20. · a body...
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A body starts from rest with uniform acceleration.
If its velocity after n second is u, then its
displacement in the last two seconds is
MENTI QUIZ - 40
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01
The speed of a body moving with uniform
acceleration is u. This speed is doubled while
covering a distance S. When it covers an
additional distance S, its speed would become
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02
A bird flies for 4 s with a velocity of |t–2| m/s a
straight line, where t is time in seconds. It covers a
distance of
(A) 2m (B) 4m
(C) 6m (D) 8m
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03
A particle is projected with velocity v0 along x-axis.
The deceleration on the particle is proportional to the
square of the distance from the origin i.e., a = –ax2.
The distance at which the particle stop is
(A) (B)
(C) (D)
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04
03
2a
u1
203
2a
u
2
03
2a
u
12 303
2a
u
A small body of mass m slides down from the top of a
hemisphere of radius r. The surface of block and
hemisphere are frictionless. The height at which the
body lose contact with the surface of the sphere is
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05
A particle is projected with a velocity v such that its
range on the horizontal plane is twice the greatest height
attained by it. The range of the projectile is (where g is
acceleration due to gravity)
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06
A man standing on the roof a house of height h throws
one particle vertically downwards and another particle
horizontally with the same velocity u. The ratio of their
velocities when they reach the earth’s surface will be
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07
A stone is projected from the ground with velocity
50 m/s at an angle of 30°. It crosses a wall after 3
sec. How far beyond the wall the stone will strike
the ground (g = 10m/sec2)
(A) 90.2m (B) 89.6m
(C) 86.6m (D) 70.2m
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08
A connon on a level plane is aimed at an angle q above
the horizontal and a shell is fired with a muzzle velocity
v0 towards a vertical cliff a distance D away. Then the
height from the bottom at which the shell strikes the side
walls of the cliff is
(A) (B)
(C) (D)
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09
2
2 2
0
2sin
2 sin
DD
u
2
2 2
0
2cos
2 cos
DD
u
2
2 2
0
2tan
2 cos
DD
u
2
2 2
0
2tan
2 sin
DD
u
A particle of mass m, initially at rest, is acted upon by a
variable force F for a brief interval of time T. It begins to
move with a velocity u after the force stops acting. F is
shown in the graph as a function of time. The curve is a
semicircle
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10
A force acts on a 2 kg object so that its position is
given as a function of time as x = 3t2+5. What is
the work done by the force in first 5 seconds
(A) 850J (B) 900J
(C) 950J (D) 875J
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11
Three blocks, A, B and C are lying on a smooth horizontal
surface, as shown in the figure. A and B have equal masses, m
while C has mass M. block A is given an brutal speed v towards
B the due to which it collides with B perfectly inelastically. The
combined mass collides with C, also perfectly inelastically 5/6th
of the initial kinetic energy is lost in whole process. What is
value of M/m
(A) 4 (B) 5
(C) 3 (D) 2
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12
A block of mass m is kept on a platform which starts
from rest with constant acceleration g/2 upward, as
shown in fig. Work done by normal reaction on
block in time t is
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13
A body of mass 1 kg falls freely from a height of 100 m
on a platform of mass 3 kg which is mounted on a
spring having spring constant k = 1.25×106N/m. The
body sticks to the platform and the spring’s maximum
compression is found to be x. Given that g = 10ms–2,
the value of x will be close to
(A) 2cm (B) 8cm
(C) 80cm (D) 40cm
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14
A body of mass m1 moving with an unknown velocity of
undergoes a collinear collision with a body of mass
m2 moving with a velocity After collision, m1 and m2
move with velocities of and respectively. If m2 =
0.5m1 and v3 =0.5v1, then v1 is
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15
1ˆ,iu
2ˆ.iu
3iu4ˆ,iu
A particle of mass ‘m’ is moving with speed ‘2v’ and collides
with a mass ‘2m’moving with speed ‘v’ in the same direction.
After collision, the first mass is stopped completely whi8le the
second one splits into two particles each of mass ‘m’, which
move at angle 45° with respect to the original direction The
speed of each of the moving particle will be
(A) (B)
(C) (D)
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16
/ 2 2u 2 2u
2u / 2u
A wedge of mass M = 4m lies on a frictionless plane. A
particle of mass m approaches the wedge with speed v.
There is no friction between the particle and the plane or
between the particle and the wedge. The maximum height
climbed by the particle on the wedge is given by
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17
Two particles, of masses M and 2M, moving, as shown, with
speed of 10m/s and 5m/s, collide elastically at the origin.
After the collision, they move along the indicated directions
with speeds v1 and v2, respectively. The values of v1 and v2
are nearly
(A) 3.2m/s and 6.3m/s
(B) 3.2m/s and 12.6m/s
(C) 6.5m/s and 6.3m/s
(D) 6.5m/s and 3.2m/s
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18
A body of mass 2 kg makes an elastic collision with
a second body at rest and continues to move in the
original direction but with one fourth of its
original speed. What is the mass of the second
body
(A) 1.8kg (B) 1.2kg
(C) 1.5kg (D) 1.0kg
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19
Body A of mass 4m moving with speed u collides
with another body B of mass 2m, at rest. The
collision is head on and elastic in nature. After the
collision the fraction of energy lost by the colliding
body A is
(A) 1/9 (B) 8/9
(C) 4/9 (D) 5/9
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20
A force F = 30+10y acts on a particle in y-direction
where F is in Newton and y in meter. Work done
by this force to move the particle from y = 0 to y =
1m is
(A) 30J (B) 5J
(C) 25J (D) 20J
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21
The elastic limit of brass is 379Mpa. What should
be the minimum diameter of a brass rod if it is to
support a 400 N load without exceeding its elastic
limit
(A) 1.16mm (B) 1.7mm
(C) 1.36mm (D) 1.00mm
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22
In an experiment, brass and steel wires of length 1m each
with area of cross section imm2 are used. The wires are
connected in series and one end of the combined wire is
connected to a rigid support and other end is subjected to
elongation. The stress required to produce a net elongation
of 0.2mm is (Given, the young’s Modulus for steel and
brass are respectively, 120×109N/m2 and 60×109N/m2)
(A) 0.2×106N/m2 (B) 8.0×106N/m2
(C) 1.8×106N/m2 (D) 1.2×106N/m2
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23
When a block of mass M is suspended by a long
wire of potential energy stored in the extended
wire is
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24
A uniform cylinder of length L and mass M having cross
sectional area A is suspended, with its length vertical, from a
fixed point by a massless spring such that it is half submerged
in a liquid of density at equilibrium position. The extension
x0 of the spring when it is in equilibrium is
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25
If ‘M’ is the mass of water that rises in a capillary
tube of radius ‘r’, then mass of water which will
rise in a capillary tube of radius ‘2r’ is
(A) 4M (B) M
(C) 2M (D) M/2
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26
The ratio of surface tensions of mercury and water is given
to be 7.5 while the ratio of their densities is 13.6. Their
contact angles, with glass, are close to 135° and 0°,
respectively. It is observed that mercury gets depressed by
an amount h in a capillary tube of radius r1. while water
raises by the same amount h in a capillary tube of radius
r2. The ratio (r1/r2), is then close to
(A) 2/3 (B) 3/5
(C) 2/5 (D) 4/5
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27
A soap bubble, having radius of 1mm, is blown from a
detergent solution having a surface tension of 2.5×10–
2N/m. The pressure inside the bubble equals at a point
Z0 below the free surface of water in a container. Taking
g = 10m/s2 density of water = 103kg/m3, the value of Z0 is
(A) 100cm (B) 10cm
(C) 1cm (D) 0.5cm
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28
A small sphere of radius ‘r’ falls from rest in a viscous
liquid. As a result, heat is produced due to viscous
force. The rate of production of heat when the sphere
attains its terminal velocity, is proportional to:
(A) r3 (B) r2
(C) r5 (D) r4
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29
Water from a pipe is coming at a rate of 100 liters
per minute. If the radius of the pipe is 5 cm, the
Reynolds number for the flow is of the order of
(density of water =1000kg/m3, coefficient of
viscosity of water = 1mPas)
(A) 106 (B) 103
(C) 104 (D) 102
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30
A submarine experiences a pressure of 5.05×106Pa at a
depth of d1 in a sea. When it goes further to a depth of
d2, it experiences a pressure of 8.08×106Pa. Then d2–
d1 is approximately (density of water = 103kg/m3 and
acceleration due to gravity = 10ms–2)
(A) 500m (B) 400m
(C) 300m (D) 600m
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31
A solid, sphere, of radius R acquires a terminal
velocity v1 when falling (due to gravity) through a
viscous fluid having a coefficient of viscosity The
sphere is broken into 27 identical solid spheres. If each
of these spheres acquires a terminal velocity, v2, when
falling through the same fluid, the ratio (v1/v2) equals
(A) 1/27 (B) 1/9
(C) 27 (D) 9
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32
Two holes of unequal diameters d1 and d2 (d1>d2) are
cut in a metal sheet. If the sheet is heated
(A) Both d1 and d2 will decrease
(B) Both d1 and d2 will increase
(C) d1 will increase, d2 will decrease
(D) d1 will decrease, d2 will increase
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33
A hollow sphere of mass ‘M’ and ‘R’ is rotating with
angular frequency ‘w’. It suddenly stops rotating and 75%
of kinetic energy is converted to heat. If ‘S’ is the specific
heat of the material in J/kg K then rise in temperature of
the sphere is (M.I. of hollow sphere = )
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34
22
3MR
A faulty thermometer has its lower fixed point
marked as –10°C and upper fixed point marked as
110°. If the temperature of the body shown in this
scale is 62°, the temperature shown on the Celsius
scale is
(A) 72°C (B) 82°C
(C) 60°C (D) 42°C
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35
The figure shows a glass tube (linear co-efficient of
expansion is a) completely filled with a liquid of volume
expansion co-efficient g. On heating length of the liquid
column does not change. Choose the correct relation
between g and a
(A) g = a
(B) g = 2a
(C) g = 3a
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36
When the temperature of a gas is raised from
27°C to 90°C, the percentage increase in the r.m.s.
velocity of the molecules will be
(A) 10% (B) 15%
(C) 20% (D) 17.5%
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37
The pressure and temperature of an ideal gas in a
closed vessel are 720 kPa and 40°C respectively. If
1/4th of the gas is released from the vessel and the
temperature of the remaining gas is raised to
353°C, the final pressure of the gas is
(A) 1440kPA (B) 1080kPA
(C) 720kPA (D) 540kPA
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38
One mole of an ideal monatomic gas requires 210J
heat to raise the temperature by 10K, when heated
at constant temperature. If the same gas is heated
at constant volume to raise the temperature by
10K then heat required is
(A) 238J (B) 126J
(C) 210J (D) 350J
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39
P-V plots for two gases during adiabatic process
are shown in the figure. Plots 1 and 2 should
correspond respectively to
(A) He and O2
(B) O2 and He
(C) He and Ar
(D) O2 and N2
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40
In an adiabatic change, the pressure P and
temperature T of a monoatomic gas are related by
the relation where c equals
(A) 5/3 (B) 2/5
(C) 3/5 (D) 5/2
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41
,CP T
Heat is supplied to a diatomic gas at constant
pressure. The ratio of DQ:DU:DW
(A) 5 : 3 : 2 (B) 5 : 2 : 3
(C) 7 : 5 : 2 (D) 7 : 2 : 5
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42
N moles of an ideal diatomic gas in a cylinder at
temperature T. Suppose on supplying heat to the gas,
its temperature remains constant but n moles get
dissociated into atoms. Heat supplied to the gas is
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43
A solid maintained at t10°C is kept in an evacuated
chamber at temperature t20°C (t2>>t1). The rate of
heat absorbed by the body is proportional to
(A) (B)
(C) (D)
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44
4 4
2 1t t 4 4
2 1( 273) ( 273)t t
2 1t t 2 2
2 1t t
A partition wall has two layers A and B in contact,
each made of a different material. They have the same
thickness but the thermal conductivity of layer A is
twice that of layer B. If the steady state temperature
difference across the wall is 60K, then the
corresponding difference across the layer A is
(A) 10K (B) 20K
(C) 30K (D) 40K
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45