A particle of mass m is dropped from a height h above the ground. At the same time another particle of
the same mass is thrown vertically upwards from the ground with a speed of √2gh . If they collide
head-on completely in elastically, the time taken for the combined mass to reach the ground, in units of √h/g
A particle of mass m and charge q is released from rest in a uniform electric field. If there is no other
force on the particle, the dependence of its speed v on the distance x travelled by it is correctly given by
(graphs are schematic and not drawn to scale)
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A particle moves such that its position vector r(t)= cosωt ˆi +sinωt ˆj where ω is a constant and t is time.
Then which of the following statements is true for the velocity v (t) and acceleration a (t) of the particle :
Consider two charged metallic spheres S1 and S2 of radii R1 and R2, respectively. The electric fields E1
(on S1) and E2 (on S2) on their surfaces are such that E1/E2 = R1/R2. Then the ratio V1(on S1)/V2 (on S2)
of the electrostatic potentials on each sphere is
A Carnot engine having an efficiency of 1/10 is being used as a refrigerator. If the work done on the
refrigerator is 10J, the amount of heat(in J)absorbed from the reservoir at lower temperature is :
A plane electromagnetic wave of frequency 25 GHz is propagating in vacuum along the z-direction. At a
particular point in space and time, the magnetic field is given by B→= 5x 10-8T. The corresponding
electric field E is (Speed of light c = 3 × 108 ms–1
A simple pendulum is being used to determine the value of gravitational acceleration g at a certain
place. The length of the pendulum is 25.0 cm and a stop watch with 1s resolution measures the time
taken for 40 oscillations to be 50 s. The accuracy in g is
A galvanometer having a coil resistance 100Ω gives a full scale deflection when a current of 1mA is
passed through it. What is the value of the resistance(in KΩ) which can convert this galvanometer into a
voltmeter giving full scale deflection for a potential difference of 10 V ?
Consider a mixture of n moles of helium gas and 2n moles of oxygen gas (molecules taken to be rigid)
as an ideal gas. Its Cp/Cv value will be :
In a double-slit experiment, at a certain point on the screen the path difference between the two
interfering waves is 1/8th of a wavelength. The ratio of the intensity of light at that point to that at the
centre of a bright fringe is
As shown in figure. When a spherical cavity (centred at O) of radius 1 is cut out of a uniform sphere of
radius R (centred at C), the centre of mass of remaining (shaded) part of sphere is at G, i.e on the
surface of the cavity. R can be determined by the equation
Two liquids of densities ρ1 and ρ2 (ρ2 = 2ρ1) are filled up behind a square wall of side 10m as shown in
figure. Each liquid has a height of 5m. The ratio of the forces due to these liquids exerted on upper part
MN to that at the lower part NO is (Assume that the liquids are not mixing) :
An electron (mass m) with initial velocity v→= v0i∧+ v0j∧ is in an electric field E= -E0k∧ . If λ0 is initial de-
Broglie wavelength of electron, its de-Broglie wave length at time t is given by :
A capacitor is made of two square plates each of side 'a' making a very small angle between them,
as shown in figure. The capacitance will be close to :
A very long wire ABDMNDC is shown in figure carrying current I. AB and BC parts are straight, long
and at right angle. At D wire forms a circular turn DMND of radius R. AB, BC parts are tangential to
circular turn at N and D. Magnetic field at the centre of circle is :
An object is gradually moving away from the focal point of a concave mirror along the axis of the mirror.
The graphical representation of the magnitude of linear magnification (m) versus distance of the object
from the mirror (x) is correctly given by (Graphs are drawn schematically and are not to scale)
A uniform sphere of mass 500 g rolls without slipping on a plane horizontal surface with its centre
moving at a speed of 5.00 cm/s. Its kinetic energy is
A transverse wave travels on a taut steel wire with a velocity of v when tension in it is 2.06 × 104N.
When the tension is changed to T, the velocity changed to v/2. The value of T is close to :
As shown in the figure, a battery of emf E is connected to an inductor L and resistance R in series. The
switch is closed at t = 0. The total charge that flows from the battery, between t = 0 and t = tc ( tc is the
time constant of the circuit) is
The first member of the Balmer series of hydrogen atom has a wavelength of 6561 Å. The wavelength
of the second member of the Balmer series (in nm) is
Three containers C1, C2 and C3 have water at different temperatures. The table below shows the final
temperature T when different amounts of water (given in liters) are taken from each container and
mixed (assume no loss of heat during the process The value of θ (in °C to the nearest integer) is____
A ball is dropped from the top of a 100 m high tower on a planet. In the last 1/2s before hitting the
ground, it covers a distance of 19 m. Acceleration due to gravity (in ms-2) near the surface on that
planet is
An asteroid is moving directly towards the centre of the earth. when at a distance of 10R (R is the
radius of the earth) from the earths centre, it has a speed of 12 km/s. Neglecting the effect of earths
atmosphere, what will be the speed of the asteroid when it hits the surface of the earth (escape velocity
from the earth is 11.2 km/s–1)? Give your answer to the nearest integer in kilometer
The series combination of two batteries, both of the same emf 10V, but different internal resistance of
20Ω and 5Ω, is connected to the parallel combination of two resistors 30Ω and RΩ. The voltage
difference across the battery of internal resistance 20Ω is zero, the value of R (in Ω) is ___