Physics

From a circular ring of mass ' M ' and radius ' R ' an arc corresponding to a 90° sector is removed. The moment of inertia of the remaining part of the ring about an axis passing through the centre of the ring and perpendicular to the plane of the ring is ' K ' times ' MR² '. Then the value of ' K ' is:

Two thin lenses are of same focal lengths (f), but one is convex and the other one is concave. When they are placed in contact with each other, the equivalent focal length of the combination will be:

For an SHM oscillator, the amplitude is 5 cm and its time period is 4 seconds. The minimum time taken by the particle to pass between points which are at distances 4 cm and 3 cm from the centre of oscillation on the same side of it will be

In the figure shown here, what is the equivalent focal length of the combination of lenses (Assume that all layers are thin)?

A series LCR circuit containing 5.0H inductor, 80μF capacitor and 40Ω resistor is connected to 230 V variable frequency ac source. The angular frequencies of the source at which power transferred to the circuit is half the power at the resonant angular frequency are likely to be:

A vertical cylindrical vessel contains a half litre of water having column height of 60 cm. If the density and bulk modulus of water are 10³ kg m^-3 and 2 * 10⁹ N m^-2 respectively, then the elastic deformation potential energy (approximately) of water, is

A particle moving in a circle of radius R with a uniform speed takes a time T to complete one revolution. If this particle were projected with the same speed at an angle ' θ ' to the horizontal, the maximum height attained by it equals 4R. The angle of projection. θ, is then given by:

An ideal gas undergoes a thermodynamic process in which internal energy (U) of the gas depends on pressure (P) of the gas as U = aP⁴, where a is a positive constant. Assuming gas to be monoatomic, the molar heat capacity of the gas for given process will be

The net impedance of circuit (as shown in figure) will be:

Two sources of sound emitting sound of nearly equal wavelengths λ₁ and λ₂ are fixed at A and B respectively. A listener moves with velocity u on the perpendicular bisector of line joining A and B. Then the number of beats heard by him per second when it is at distance 2l from A and B, is (Speed of sound = C)