In the equation y = a sin (ωt + kx), the dimensional form ula of ω is
An electron (mass = 9 x 10-31 kg, charge = 1.6 x 10-19 C) moving with a velocity of 106 m/s enters a magnetic field. If it describes a circle of radius 0.1m, then strength ofmagnetic field must be
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The component of vector A = 2i + 3j along the vector i + j is
When an electron jumps from the fourth orbit to the second orbit, one gets the
A 70 kg man stands in contact against the inner wall of a hollow cylindrical drum of radius 3 m rotating about its vertical axis with 200 rev/min. The coefficient of friction between the wall and his clothing is 0.15. When the floor is suddenly removed, what is the minimum rotational speed o f the cylinder to enable the man to remain stuck to the wall with out falling (approximately)?
A ball of mass 150 g, moving with an acceleration 20 m/s2, is hit by a force, which acts on it for 0.1 sec. The impulsive force is
A block of mass m moving at a velocity v collides with another block of mass 2m at rest. The lighter block comes to rest after collision. Find the coefficient of restitution.
Two identical galvanometers are taken, one is to be converted into an ammeter and other into a milliammeter. Shunt of milliammeter compared to ammeter is
A circular disc rolls down an inclined plane. The ratio of rotational kinetic energy to total kinetic energy is
Let Ea be the electric field due to a dipole in its axial plane distant ℓ and Eq be the field in the equatorial plane distant ℓ , then the relation between Ea and Eq will be
A metallic sphere of diameter 10 cm and mass 0.5 kg is fixed to one end of a thin rod of length 50 cm and mass 1 kg as shown in the given figure. The rod with the sphere will balance horizontally, when it is supported at a point whose distance from the free end of the rod is
The moment of inertia of a disc of mass m and radius r about an axis, which is tangential to the circumference of the disc and parallel to its diameter is
A cylinder of height 20 m is completely filled with water. The velocity of efflux of water (in ms-1) through a small hole on the side wall of the cylinder near its bottom is
A convex lens of focal length 40 cm is held coaxially 12 cm above a mirror of focal length 18 cm. An object held x cm above the lens gives rise to an image coincident with it. Then x is equal to :
In a circuit, L, C and R are connected in series with an alternating voltage source of frequency f. The current leads the voltage by 45°. The value of C is
Under a constant torque the angular momentum of a body changes from A to 4A in 4 second. The torque on the body will be
22320 cal of heat is supplied to 100 g of ice at 0°C. If the latent heat of fusion of ice is 80 cal g-1 and latent heat of vaporization of water is 540 cal g-1, the final amount of water, thus obtained and its temperature respectively are
The height at which the acceleration due to gravity becomes g/9 (where g = the acceleration due to gravity on the surface of the earth) in terms of R, the radius of the earth, is
Standing waves are produced in 10 m long stretched string. If the string vibrates in five segments and wave velocity is 20 ms-1, then its frequency will be
When a wave travels in a medium the particles displacement is given by the equation y = 0.03 sin π(2t - 0.01x), where x and y are in seconds. The wavelength of the wave is
A hemisphere surface of radius R is placed in uniform electric field of intensity E parallel to the axis of its circular plane, What will be the electric flux φ through the hemisphere surface?
The specific heat capacity of a metal at low temperature (T) is given as A 100 g vessel of this metal is to be cooled from 20 K to 4 K by a special refrigerator operating at room temperature (27°C). The amount of work required to cool in vessel is
A charged particle q is shot towards another charged particle Q, which is fixed, a speed v. It approaches Q up to a closest distance r and then returns. If q were given a speed of 2v, then closet distance of approach would be
Two particles are oscillating along two close parallel straight lines side by side, with the same frequency and amplitudes. They pass each other, moving in opposite directions when their displacement is half of the amplitude. The mean positions of the two particles lie on a straight line perpendicular to the paths of the two particles. The phase difference is
In a solenoid, if number of turns is doubled, then self-inductance will become
What is the acceleration of a projectile at its highest point
If a source is transmitting electromagnetic wave of frequency 8.2 x 106 Hz, then wavelength of electromagnetic waves transmitting from the source will be
A block A of mass 7 kg is placed on a frictionless table. A thread tied to it passes over a frictionless pulley and carries a body B of mass 3 kg at the other end. The acceleration of the system is (given g = 10 ms-2)
In a Young’s experiment, two coherent sources are placed 0.90 mm apart and the fringes are observed one metre away. If it produces the second dark fringe at a distance of 1 mm from the central fringe, then wavelength of monochromatic light used would be
A uniform magnetic field acts at right angles to the direction of motion of electron. As a result, the electron moves in a circular path of radius 2 cm. If the speed of electron is doubled, then the radius of the circular path will be