Which of the following pairs of physical quantities have same dimension?

Two objects of masses m₁ and m₂ fall from the heights h₁ and h₂ respectively. The ratio of the magnitude of their momenta when they hit the ground is

The distance travelled by a particle starting from rest and moving with an acceleration \({4\over3}ms^{-2}\), in the third second is _____________.

Force acting on the particle moving with constant speed is

What is the minimum velocity with which a body of mass m must enter a vertical loop of radius R so that it can complete the loop?

A particle is moving with a constant velocity along a line parallel to positive X-axis. The magnitude of its angular momentum with respect to the origin is

A mass M is moving with a constant velocity along a line parallel to the z-axis away from the origin. Its angular momentum with respect to the origin _____________.

The magnitude of the Sun’s gravitational field as experienced by Earth is

For a given material, the rigidity modulus is \(\left( \frac { 1 }{ 3 } \right) \)^rd of Young’s modulus. Its Poisson’s ratio is

When the distance between the two atoms becomes '\(\gamma_{0}\)' then the inter atomic force will be____________.

The graph between volume and temperature in Charles’ law is

A particle of mass m is moving with speed u in a direction which makes 60° with respect to x axis. It undergoes elastic collision with the wall. What is the change in momentum in x and y direction?

A simple pendulum is suspended from the roof of a school bus which moves in a horizontal direction with an acceleration a, then the time period is

A body of mass 1 kg is executing SHM given by, x = 4 Cos\(\left( 100t+\frac { \pi }{ 2 } \right) \)cm. Whatis the velocity?

A uniform rope having mass m hangs vertically from a rigid support. A transverse wave pulse is produced at the lower end. Which of the following plots shows the correct variation of speed v with height h from the lower end?

What is 1 light year?

A water fountain on the ground sprinkles water all around it. If the speed of the water coming out of the fountain is v, calculate the total area around the fountain that gets wet.

A wooden box is lying on an inclined plane. What is the coefficient of friction if the box starts sliding when the angle of inclination is 45°.

Which unit is used to measure electrical energy?

Give an example to show that the following statement is false. 'any two forces acting on a body can be combined into single force that would have same effect'.

State Pascal’s law in fluids.

State the second law of thermodynamics in terms of entropy.

Define frequency of simple harmonic motion.

How can we distinguish experimentally between longitudinal and transverse waves?

Write the role of physics in technology.

Define angular displacement and angular velocity.

Consider a horse attached to the cart which is initially at rest. If the horse starts walking forward, the cart also accelerates in the forward direction. If the horse pulls the cart with force F_h in forward direction, then according to Newton's third law, the cart also pulls the horse by equivalent opposite force F_c = F_h in backward direction. Then total force on 'cart+horse' is zero. Why is it then the 'cart+horse' accelerates and moves forward?

Give an example in which a force does work on a body but fails to change its K.E.

To maintain a rotor at a uniform angular speed of 200 rad s^-1, an engine needs to transmit a torque of 180 Nm. What is the power required by the engine? Assume that the engine is 100% efficient.

Draw graphs showing the variation of acceleration due to gravity with
(i) height above the earth's surface
(ii) depth below the earth's surface.

How is skating possible on snow?

Estimate the total number of molecules inclusive of oxygen, nitrogen, water vapour and other consituents in a room of capacity 30 m³ at a temperature of 30°C and 1 atmosphere pressure.

An observer observes two moving trains, one reaching the station and other leaving the station with equal speeds of 8 m s⁻¹. If each train sounds its whistles with frequency 240 Hz, then calculate the number of beats heard by the observer.

The force F acting on a body moving in a circular path depends on mass of the body (m), velocity (v) and radius (r) of the circular path. Obtain the expression for the force by dimensional analysis method. (Take the value of k = 1)

Explain in details the subtraction of two vectors.

Explain the need for banking of tracks.

Find the work done and power of an car engine which can maintain a speed of 40 ms^-1 for a mass of a car 2\(\times\)10³ kg on a rough level road to 2 km. The coefficient of friction is 0.05.

A solid cylinder of mass 20 kg rotates about its axis with angular speed 100 rad/s. The radius of the cylinder is 0.25m. Calculate the kinetic energy associated with the rotation of the cylinder.

Calculate the energy of the
(i) Moon orbiting the Earth and
(ii) Earth orbiting the Sun.

Obtain an equation of continuity for a flow of fluid on the basis of conservation of mass.

Give some examples of irreversible processes.

0.014 kg of nitrogen is enclosed in a vessel at a temperature of 27°C. How much heat has to be transferred to double the rms speed of its molecules.

Show that for a particle executing simple harmonic motion
a. the average value of kinetic energy is equal to the average value of potential energy.
b. average potential energy = average kinetic energy = \(\frac{1}{2}\) (total energy)
Hint: average kinetic energy =< kinetic energy > = \(\frac{1}{T} \int_{0}^{T}\)(Kineticenergy) dt and
average Potential energy = < Potential energy > = \(\frac{1}{T} \int_{0}^{T}\) (Potential energy) dt