Consider two hot bodies B1 and B2 which have temperatures 100°C and 80°C respectively at t = 0. The temperature of the surroundings is 40°C. The ratio of the respective rates of cooling R1 and R2 of these two bodies at t = 0 will be
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The value of n so that vectors and may be coplanar, will be
A primary cell has an e.m.f. of 1.5 volt. When short-circuited it gives a current of 3 ampere. The internal resistance of the cell is
A particle of mass 100g tied to a string is rotated along a circle of radius 0.5 m. The breaking tension of string is 10 N. The maximum speed which particle can be rotated without breaking the string is
An ideal gas A and a real gas B have their volumes increased from V to 2 V under isothermal conditions. The increase in internal energy
An inclined plane makes an angle of 30° with the horizontal. A solid sphere rolling down this inclined plane from rest without slipping has a linear acceleration equal to
A straight rod of length L extends from x = a to x = L + a. Find the gravitational force it exerts on a point mass m at x = 0 if the linear density of rod μ = A + Bx2
Two bodies of mass 10 kg and 5 kg moving in concentric orbits of radius R and r such that their periods are the same. Then, the ratio between .their centripetal acceleration is
When soundwaves travel from air to water, which one of the following remains constant?
A cylindrical vessel of radius r containing a liquid is rotating about a vertical axis through the centre of circular base. If the vessel is rotating with angular velocity ω, then what is difference of the heights o liquid at centre of vessel and edge
The electrostatic potential inside a charged spherical ball is given by φ= ar2 + b where r is the distance from the centre and a, b are constants. Then the charge density inside the ball is:
An AC circuit contains a resistance R, capacitance C and inductance L in series with a source of emf ξ = ξ0 sin (ωt + φ)The current through the circuit is maximum, when
If Q, E and W denote respectively the heat added,change in internal energy and the work done in aclosed cyclic process, then
A solid ball of density ρ1 and radius r falls vertically through a liquid of density ρ2. Assume that the viscous force acting on the ball is F = krv, where k is a constant and v its velocity. What is the terminal velocity of the ball?
After 300 days, the activity of a radioactive sample is 5000 dps (disintegrations per sec). The activity becomes 2500 dps after another 150 days. The initial activity of the sample in dps is
An organ pipe, open from both ends produced 5 beats/s when vibrated with a source of frequency 200 Hz in its fundamental mode. The second harmonic of the same pipe produces 10 beats/s with a source of frequency 420 Hz. The fundamental frequency of pipe is
Monochromatic light of frequency 6.0 x 1014Hz is produced by a laser. The power emitted is 2 x 10-3 W. The number of photons emitted, on the average, by the source per second is
What is the total flux from the surface of cylinder of radius R and length L which is placed in a uniform electric field E parallel to cylinder axis?
A steel wire of length 20 cm and uniform cross-section 1 mm2 is tied rigidly at both the ends. The temperature of the wire is altered from 40°C to 20°C. Coefficient of linear expansion for steel a= 1.1 x 10-5/°C and Y for steel is 2.0 x 1011 N/m2. The change in tension of the wire is
A charge Q is distributed over two concentric hollow spheres of radii r and R ( R > r ) such that, their surface densities are equal. Find the potential at the common centre k = (4πε0)-1
The pressure P of an ideal gas and its mean K.E. per unit volume are related as
A metal sample carrying a current along X-axis with density Jx is subjected to a magnetic field Bz (along z-axis). The electric field Ey developed along Y-axis is directly proportional to Jx as well as Bz, The constant of proportionality has SI unit
A linearly polarised electromagnetic wave given as E = E0 i cos(kz - ωt) is incident normally on a perfectly reflecting infinite wall at z = a. Assuming that the material of the wall is optically inactive, the reflected wave will be given as
In the given figure, Q is the position first bright range towards right from OP is the position of 5th b right fringe on the other side of O with respect to Q. If wavelength of used light is 6000 Å, then value of S1B will be
A motor car is travelling at 30 m/s on a circular road of radius 500 m. It is increasing in speed at the rate of 2 m/s2. Then the acceleration of the car will be