Mix Test - 1...

A small solid sphere of radius R made of a material of bulk modulus B is surrounded by an incompressible liquid in a cylindrical container. A massless piston of area A floats on the surfaces of the liquid. Find the magnitude of frictional change in the radius of the sphere (dR/R) when a mass M is placed slowly on the piston to compress the liquid.

Find the value of r so that maximum power is generated in external circuit.

The air of density ρ and moving with a velocity v strikes perpendicularly the inclined surface of area A and of a wedge kept on a horizontal surface. The mass of the wedge is m. Assuming the collisions to be perfectly inelastic, the minimum value of the coefficient of friction between the wedge and the ground so that the wedge does not move is: (Assume that mass of particles of air is negligible)

In a YDSE apparatus, the source (wavelength λ) is kept as shown in the figure. None of the slits receives direct light but gets it after reflection by mirrors as shown in the figure. If d = 100λ and D = 50000λ, then the distance of central maxima from the centre of the screen is:

A straight small object is kept in front of a convex lens, as shown in the figure. Which among the following shows the right image of the object?

Two identical balls of radii r are kept on a horizontal plane with their centres d distance apart. A third ball, identical to previous ones, collides elastically with both the balls symmetrically as shown in the figure. If the third ball comes to rest after the collision, d should be

One mole of an ideal gas is carried through a thermodynamic cycle as shown in the figure. The cyclic process consists of an isochoric, an isothermal and an adiabatic process. Find the adiabatic exponent of gas.

The figure below shows roughly how the force (F) between two adjacent atoms in a solid varies with separation (r).

(i) OQ is equilibrium separation.
(ii) Hooke`s law is obeyed around P
(iii) The potential energy of the atom is the gradient of the graph at all points.
(iv) The energy to separate the atoms completely is obtained from the area enclosed below the axis of r.

In the situation as shown in figure, if acceleration of B is 'a', then find the acceleration of A.

A semicircular disc of mass 'M' and radius 'R' is let from rest from a vertical position as shown. Assuming that the disc does not slip, the initial magnitude of angular acceleration of the disc will be:

A solid cone of height H and radius R suspended by a string is just submerged in a liquid of density p as shown in the figure. The magnitude of the net force applied by the liquid on the curved surface of the cone is: (P_o is the atmospheric pressure)

In a sample of hydrogen like atoms all of which are in ground state, a photon beam containing photons of various energies is passed. In absorption spectrum, five dark lines are observed. The number of bright lines in the emission spectrum will be: (Assume that all transitions take place)

In a sample of rock, the ratio of ²⁰⁶Pb to ²³⁸U nuclei is found to be 0.5. The age of the rock is: (Assume that all the Pb nuclides in the rock was produced due to the decay of Urarium nuclides and

A thin plane convex glass lens ( = 1.5) has its plane surface silvered and R is the radius of curvature of the curved part. Then, which of the following ray diagrams is the correct representation for an object placed at O?

Initially, a spring is compressed by distance x₀ from equilibrium position. At this compression, the block is given velocity, so that compression in the spring increases and the block starts executing S.H.M. (Spring constant is K). Equation of motion of the block is:

A sample of radioactive material has mass m, decay constant , molecular weight M and Avogadro constant N_A. The initial activity of the sample is

The instantaneous height and position of a projectile are given by x = 6t, y = 8t - 5t² metre. What is the initial speed of the projectile? (`t` is in seconds)

The fundamental frequency of a sonometer wire of length `` is f_o. A bridge is now introduced at a distance of from the centre of the wire . The number of beats heard, if both sides of the bridges are set into vibration in their fundamental modes, is

A capillary tube of radius `r` is immersed in water and water rises in it to a height `h`. The mass of water in the capillary tube is `m`. Another capillary of radius 2r is immersed in water. The mass of water that will rise in this tube is:

A plano-concave lens fits into a plano-convex lens and their plane surfaces are parallel to each other. If lenses are made of different materials having refractive indices and and the radius of curvature of the curved surfaces is R, find the focal length of the system.

There is a man of mass 100 kg sitting on a motorbike of mass 150 kg. The distance between axles of the wheels (wheelbase) is 1.5 m. The common centre of mass of the man and motorbike is at a height of I m above ground and at a distance of 0.6 m from the vertical line going through the rear axle. Then, (Take g = 10 m/s²)

A point object is projected from a point on the principal axis of a concave mirror of focal length 20 cm with a speed of m/s at an angle of tan^-1 2 with the principal axis as shown in figure. Choose the correct option. (Consider the moment just after projection)

The molar heat capacity C of an ideal gas in a process is given by C = a/T, where `a` is a constant. If the work done by one mole of gas during heating from T_o to nT_o through the same process will be

A satellite is projected with velocity times its escape speed from Earth`s surface. The initial velocity of the satellite is parallel to the surface of Earth. The maximum distance of the satellite from the centre of Earth will be

A particle is projected from point A at an angle of 53^o with horizontal. At the same time, the wedge starts from rest and moves with constant acceleration 'a' as shown. The value of 'a' for which the particle strikes the plane perpendicular to it at P is:

A transverse wave is travelling along negative y-axis whose snap shot is given at any instant of time t. Find out the points which are having velocity in negative x-direction.

Energy required to remove one electron from neutral helium atom is E₁ eV. Energy required to remove both electrons form a neutral helium atom is

A small air bubble is inside a transparent-sphere made of two different material having refractive indices and . The radius of sphere is 10 cm. If the position of bubble is 8 cm from the bottom, then what will be the approximate apparent depth of the bubble when viewed normal?

A particle is projected with a velocity of 10 ms^-1 at an angle 37^o with horizontal. A bird moves along the path of projected particle with constant speed of 4 ms^-1. Find the acceleration of bird when it is at the highest point of path of particle. (Take g = 10 ms^-2)

The mass of the astronauts in a space station cannot be checked with the scales used on the Earth. Instead we use a spring balance, which oscillates when a mass is suspended from it. Imagine a seat of a mass of 20 kg, which oscillates with a frequency of 2 Hz. After the astronaut sits in the seat, the frequency decreases to 1 Hz. How much is the mass of the astronaut?