Physics

A solid sphere of radius R carries a charge Q + q distributed uniformly over its volume. A very small point like piece of it of mass m gets detached from the bottom of the sphere and falls down vertically under gravity. This piece carries charge q. If it acquires a speed v when it has fallen through a vertical height h (see figure), then: (assume the remaining portion to be spherical)

For a concave lens of focal length f, the relation between object and image distances u and is v, respectively, from its pole can best be represented by ( u = v is the reference line): (Ray Optics)

The value of the acceleration due to gravity is g₁ at a height h = R/2 (R = radius of the earth) from the surface of the earth. It is again equal to g₁ at a depth d below the surface of the earth. The ratio (d/R) equals:

A bullet of mass 5 g, traveling with a speed of 210 m/s, strikes a fixed wooden target. One half of its kinetic energy is converted into heat in the bullet while the other half is converted into heat in the wood. The rise of temperature of the bullet if the specific heat of its material is 0.030cal/(g- °C)(1cal = 4.2 * 10⁷ergs) close to:

With increasing biasing voltage of a photodiode, the photocurrent magnitude:

In a resonance tube experiment when the tube is filled with water up to a height of 17.0 cm from bottom, it resonates with a given tuning fork. When the water level is raised the next resonance with the same tuning fork occurs at a height of 24.5 cm. If the velocity of sound in air is 330 m/s, the tuning fork frequency is:

A wheel is rotating freely with an angular speed ω on a shaft. The moment of inertia of the wheel is I and the moment of inertia of the shaft is negligible. Another wheel of moment of inertia 3I initially at rest is suddenly coupled to the same shaft. The resultant fractional loss in the kinetic energy of the system is:

A balloon is moving up in air vertically above a point A on the ground. When it is at a height h₁, a girl standing at a distance d (point B) from A (see figure) sees it at the angle 45° with respect to the vertical. When the balloon climbs up a future height h₂, it is seen at the angle 60° with respect to the vertical if the girl moves further by a distance 2.464 d (point C). Then the height h₂ is (given tan 30° = 0.5774) :

A hollow spherical shell at outer radius R floats just submerged under the water surface. The inner radius of the shell is r. If the specific gravity of the shell material is 27/8 w.r.t water, the value of r is.

What is the unit of refractive index?