JEE Advanced Ph...

An engine whistling at a constant frequency n₀ and moving with a constant velocity goes past a stationary observer. As the engine crosses him, the frequency of the sound heard by him changes by a factor f. The actual difference in the frequency of the sound heard by him before and after the engine across him is

A ball of density ρ₀ falls from rest from point P onto the surface of a liquid of density ρ in time T. It enters the liquid stops moves up and returns to P in a total time 3T. Neglect viscosity, surface tension and splashing. The ratio p/p₀ is equal to

When an object is placed in front of a concave mirror of focal length f, a virtual image is produced with a magnification of 2. To obtain a real image with a magnification of 2. The object has to be moved by a distance equal to

A solid cube is placed on a horizontal surface. The coefficient of friction between them is μ, where μ < 1/2 . A variable horizontal force is applied on the cube’s upper face, perpendicular to one edge and passing through the mid-point of that edge. The maximum acceleration with which it can move without toppling is

A spherical body of mass m, radius r and moment of inertia I about its centre moves along the x-axis. Its centre of mass moves with velocity = v₀ and it rotates about its centre of mass with angular velocity ω₀.L_O = lω₀ + mv_or . The angular momentum of the body about the origin O is

The coefficient of linear expansion for a certain metal varies with absolute  temperature as  α = aT. If L_o = 1 m is the initial length of the metal and the temperature of metal is changed from 27^oC to 127^oC, then final length is (where a = 2 × 10^-5 K⁻²)  

The radiations that can ionize the matter are

A billiard player hits a billiard ball of mass m and radius r lying at rest on the billiard table. When the cue hits the ball horizontally with force F at a height (r + h) from the table top the ball rolls without slipping. h is given as

For c = 3a = 2b, the magnetic field at point P is

A conducting rod is rotated by means of strings in a uniform magnetic field with constant angular velocity as shown in the figure. Potential of points A, B and C are V_A, V_B and V_C respectively. Then