13882.Starting from the centre of the earth having radius R, the variation of g (acceleration due to gravity) is shown by
Explanation:
$g_{in} = g_o\dfrac{r}{R}$ g0 is g at surface
$g_{in} = g_o\left(\dfrac{R^2}{r^2}\right)$
13887.A body cools from a temperature 3T to 2T in 10 minutes. The room temperature is T. Assume that Newtons law of cooling is applicable. The temperature of the body at the end of next 10 minutes will be
T
$\dfrac{7}{4}$T
$\dfrac{3}{2}$T
$\dfrac{4}{3}$T
Explanation:
$\triangle T = \triangle T_0e^{–\lambda t}$
$T = 2Te^{–\lambda(10 \ min.)}$
$\triangle T = 2Te^{–\lambda(20 \ min.)} = 2T\left(\dfrac{1}{2}\right)^2 = \dfrac{T}{2}$
$T_f = T + \dfrac{T}{2} = \dfrac{3T}{2}$
13893.Three sound waves of equal amplitudes have frequencies (n – 1), n, (n + 1). They superimpose to give beats. The number of beats produced per second will be
2
1
4
3
Explanation:
no. of beats = 1
(HCF of beat frequencies)
no. of beats = 1
(HCF of beat frequencies)
13905.Two identical glass (μg = 3/2) equiconvex lenses of focal length f each are kept in contact. The space between that two lenses in filled with water (μw = 4/3). The focal length of the combination is
3f / 4
f / 3
f
4f / 3
Explanation:
$\dfrac{1}{f} = \left(\dfrac{3}{2}–1\right)\dfrac{2}{R} = \dfrac{1}{R}$
$\dfrac{1}{f} = \left(\dfrac{4}{3}–1\right)\left\{–\dfrac{2}{R}\right\} = –\dfrac{2}{3R}$
$\dfrac{1}{f_{eq}} = \dfrac{1}{f}–\dfrac{2}{3f} + \dfrac{1}{f} = \dfrac{3 – 2 + 3}{3f} = \dfrac{4}{3f}$
$f_{eq} = \dfrac{3f}{4}$
23241.If n denotes a positive integer, h the Planck’s constant, q the charge and B the magnetic field, then the quantity $\dfrac{nh}{2\pi qB}$ has the dimension of
area
length
speed
acceleration
23248.Let [ε0] denote the dimensional formula of the permittivity of vacuum. If M = mass, L = length, T = time and A = electric current, then:
[ε0] = [M–1L–3T4A2]
[ε0] = [M–1L2T–1A–2]
[ε0] = [M–1L2T–1A]
[ε0] = [M–1L–3T2A]
23258.Match List–I (Fundamental Experiment) with List–II (its conclusion) and select the correct option from the choices given below the list:
| List – I | List – II | ||
|---|---|---|---|
| (A) | Franck–Hertz experiment | (i) | Particle nature of light |
| (B) | Photo–electric experiment | (ii) | Discrete energy levels of atom |
| (C) | Davison–Germer experiment | (iii) | Wave nature of electron |
| (iv) | Structure of atom |
(A) – (i) (B) – (iv) (C) – (iii)
(A) – (ii) (B) – (iv) (C) – (iii)
(A) – (ii) (B) – (i) (C) – (iii)
(A) – (iv) (B) – (iii) (C) – (ii)
23263.Helium gas goes through a cycle ABCDA (consisting of two isochoric and isobaric lines) as shown in figure. Efficiency of this cycle is nearly
(Assume the gas to be close to ideal gas)
(Assume the gas to be close to ideal gas)
15.4%
9.1%
10.5%
12.5%
23269.A Carnot engine, whose efficiency is 40%, takes in heat from a source maintained at a temperature of 500K. It is desired to have an engine of efficiency 60%, then the intake temperature for the same exhaust (sink) temperature must be :
efficiency of Carnot engine cannot be made larger than 50%
1200 K
750 K
600 K
23270.An ideal gas is compressed to half its initial volume by means of several processes. Which of the process results in the maximum work done on the gas?
Isothermal
Adiabatic
Isobaric
Isochoric
23279.A body is traveling in a circle at constant speed. It
has constant velocity.
has no acceleration
has an inward acceleration
has an outward radial acceleration
23281.A particle P is moving in a circle of radius ‘a’ with uniform speed v. C is the centre of the circle and AP is diameter. The angular velocity of P about A and C are in the ratio
1 : 1
1 : 2
2 : 1
4 : 1
23297.When the angular velocity of a uniformly rotating body has increased thrice the resultant of forces applied to it increases by 60 N. find the acceleration of the body in two cases if the mass of the body is 3 kg
2.5 m s–2, 7.5 m s–2
7.5 m s–2, 67.5 m s–2
5 m s–2, 45 m s–2
2.5 m s–2, 22.5 m s–2
23306.A car has a linear velocity v on a circular track of radius r. If its speed is increasing at a rate of a m/s2, then its resultant acceleration will be
$\sqrt{\left(\dfrac{v^2}{r}\right)^2 + a^2}$
$\sqrt{\left(\dfrac{v^2}{r}\right)^2 – a^2}$
$\left(\dfrac{v^2}{r}\right)^2 + a^2$
$\left(\dfrac{v^2}{r}\right)^2 – a^2$
23327.A motor cyclist moving with a velocity of 75 km/hr on a flat road takes a turn on the road at a point where the radius of curvature of the road is 20 m. If the g is 10 m/s2 the maximum angle of banking with vertical for no skidding is
tan–1 (6)
tan–1 (2)
tan–1 (12)
tan–1 (4)
23344.An electric fan has blades of length 30 cm as measured from the axis of rotation. If the fan is rotating at 1200 r.p.m., then the acceleration of a point on the tip of the blade is (take $π$2 = 10)
1600 m/s2
3200 m/s2
4800 m/s2
6000 m/s2
23364.In order to cause something to move in a circular path, we must apply
Inertial force
Centripetal force
Centrifugal force
Gravitational force
23376.When particle revolves with uniform speed on a circular path
no force acts on it
no acceleration acts on it
no work is done by it
its velocity is constant
23378.A plank with a box on it at one end is gradually raised about the other end. As the angle of inclination with the horizontal reaches 30º, the box starts to slip and slides 4.0 m down the plank in 4.0 s. The coefficients of static and kinetic friction between the box and the plank will be, respectively
0.4 and 0.3
0.6 and 0.6
0.6 and 0.5
0.5 and 0.6
23418.A photocell is illuminated by a small bright source placed 1 m away. When the same source of light is placed 1/2 m away , the number of electrons emitted by photocathode would
increase by a factor of 4
decrease by a factor of 4
increase by a factor of 2
decrease by a factor of 2
23458.A capacitor of 2 μF is charged as shown in the diagram. When the switch S is turned to position 2, the percentage of its stored energy dissipated is
75%
80%
0%
20%
23475.Shown in the figure below is a meter–bridge set up with null deflection in the galvanometer.
The value of the unknown resistor R is
The value of the unknown resistor R is
220 Ω
110 Ω
55 Ω
13.75 Ω
23479.Across a metallic conductor of non–uniform cross section a constant potential difference is applied. The quantity which remains constant along the conductor is
Current density
Current
Drift velocity
Electric field
23491.A 5V battery with internal resistance 2 Ω and a 2V battery with internal resistance 1 Ω are connected to a 10 Ω resistor as shown in the figure.
The current in the 10 Ω resistor is
The current in the 10 Ω resistor is
0.03 A P1 to P2
0.03 A P2 to P1
0.27 A P1 to P2
0.27 A P2 to P1
23505.If a velocity has both perpendicular and parallel components while moving through a magnetic field, what is the path followed by a charged particle?
Circular
Elliptical
Linear
Helical
23517.Sensitivity of a moving coil galvanometer can be increased by
decreasing the number of turns of coil
increasing the number of turns of coil
decreasing the area of a coil
by using a weak magnet
23524.Hysteresis loops for two magnetic materials A and B are given below:
These materials are used to make magnets for electric generators, transformer core and electromagnet core. Then it is proper to use:
These materials are used to make magnets for electric generators, transformer core and electromagnet core. Then it is proper to use:
A for electromagnets and B for electric generators
A for transformers and B for electric generators
B for electromagnets and transformers
A for electric generators and transformers
23531.Curie temperature is the temperature above which
a ferromagnetic material becomes paramagnetic.
a paramagnetic material becomes diamagnetic.
a ferromagnetic material becomes diamagnetic.
a paramagnetic material becomes ferromagnetic.
23545.Pick out the longest wavelength from the following types of radiations.
Blue light
Gamma rays
X–rays
Red light
23547.A plane electromagnetic wave of frequency 20 MHz travels through a space along x direction. If the electric field vector at a certain point in space is 6 V m–1, what is the magnetic field vector at that point?
2 × 10–8 T
1/2 × 10–8 T
2 T
1/2 T
23561.Assertion : The energy (E) and momentum (p) of a photon are related by p = E/c.
Reason : The photon behaves like a particle.
Reason : The photon behaves like a particle.
both assertion and reason are true and reason is the correct explanation of assertion.
both assertion and reason are true but reason is not the correct explanation of assertion.
assertion is true but reason is false.
assertion and reason are false.
26163.The root mean square speed of hydrogen molecules at 300 K is 1930 m/s. then the root mean square speed of oxygen molecules at 900 K will be
1930$\sqrt{3}$ m/s
836 m/s
643 m/s
$\dfrac{1930}{\sqrt{3}}$ m/s
26173.One any planet, the presence of atmosphere implies [νrms = root mean square velocity of molecules and νe = escape velocity]
vrms << ve
vrms > ve
vrms = ve
vrms = 0
26194.The average translational K.E. of the molecules in a sample of oxygen at 300K is 6 × 10–20 J. what is the average translational energy at 750 K?
2 × 10–19 J
1.5 × 10–19 J
3 × 10–18 J
3.5 × 10–21 J
26196.Mean kinetic energy of perfect gas is
$\propto$ T
$\propto$ T2
$\propto \dfrac{1}{T}$
$\propto \dfrac{1}{T^2}$
26206.Kepler’s second law regarding constancy of arial velocity of a planet is a consequence of the law of conservation of
energy
angular momentum
linear momentum
none of these
26229.If R is radius of the earth and g the acceleration due to gravity on the earth’s surface, the mean density of the earth is
$\dfrac{4\pi G}{2gR}$
$\dfrac{3\pi G}{4gR}$
$\dfrac{3g}{4\pi RG}$
$\dfrac{4\pi RG}{3g}$
26242.What would be the duration of the year if the distance between the earth and the sun gets doubled?
1032 days
129 days
365 days
730 days
26277.The wavelength of maximum energy released during an atomic explosion was 2.93 × $10^{-10}$m. The maximum temperature attained must be (Wien’s constant = 2.93 × $10^{-3}$mK)
5.86 × $10^{7}$K
$10^{-13}$ K
$10^{-7}$ K
$10^{7}$ K
26293.Two spheres made of same material have radii in the ratio 2:1. if both the spheres are at same temperature, then what is the ratio of heat radiation energy emitted per second by them?
1: 4
4: 1
3: 4
4: 3
26330.According to Wien’s law
λm T = constant
$\dfrac{\lambda_{m}}{T}$ = constant
$\dfrac{T}{\lambda_{m}}$ = constant
T + λm = constant
26346.512 calories of radiation is incident on a body. It absorbs 220 calories the coefficient of emission is
0.43
0.57
1.7
0.34