Planck's constant (h), speed of light in vacuum (c) and Newton's gravitational constant (G) are taken as three fundamental constants. Which of the following combinations of these has the dimension of length?

A ball is projected vertically upwards with a velocity v. It comes back to ground in time t. Which v-t graph shows the motion correctly?

A man throws balls with the same speed vertically upwards one after the other at an interval of 2 seconds. What should be the speed of the throw so that more than two bails are in the sky at any time? (Given g = 9.8m/s²)

Two blocks of masses m and 2m are placed on a smooth horizontal surface as shown. In the first case only a force F₁ is applied from the left. Later only a force F₂ is applied from the right. If the force acting at the interface of the two blocks in the two cases is same, then F₁ :F₂ is

Two equal masses m₁ and m₂ moving along the same straight line with velocities +3 m/s and -5 m/s respectively collide elastically. Their velocities after the collision will be respectively _______________.

From a disc of radius R a mass M, a circular hole of diameter R, whose rim passes through the center is cut. What is the moment of inertia of the remaining part of the disc about a perpendicular axis passing through it

The sum of moments of masses of all the particles in a system about the center of mass is _____________.

According to Kepler’s second law, the radial vector to a planet from the Sun sweeps out equal areas in equal intervals of time. This law is a consequence of

Which of the following is not a scalar?

Two drops of equal radius coalesce to form a bigger drop. What is ratio of surface energy of bigger drop to smaller one?

In an isochoric process, we have

A sample of gas consists of \(\mu\)₁ moles of monoatomic molecules, \(\mu\)₂ moles of diatomic molecules and \(\mu\)₃ moles of linear triatomic molecules. The gas is kept at high temperature. What is the total number of degrees of freedom?

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

Two simple pendulums of time periods 2.0 s & 2.1 s are made to vibrate simultaneously. They are in phase initially, after how may vibrations are there in the same phase?

Let y = \(\frac{1}{1+x^2}\) at t = 0 s be the amplitude of the wave propagating in the positive x-direction. At t = 2 s, the amplitude of the wave propagating becomes \(y=\frac{1}{1+(x-2)^{2}}. \) Assume that the shape of the wave does not change during propagation. The velocity of the wave is

State the number of significant figures in 2.64\(\times\)1024 kg

An object is thrown vertically downward. What is the acceleration experienced by the object?

The position of the particle is represented by y = ut - \(\frac { 1 }{ 2 } \) gt²
(a) What is the force acting on the particle?
(b) What is the momentum of the particle?

KE. of a body is increased by 300 %. Find the % increase in its momentum.

A small particle of mass m is projected with an initial velocity v at an angle \(\theta\) with x-axis in X-Y plane as shown in Figure.

Find the angular momentum of the particle.

State Hooke’s law of elasticity. 

A Carnot engine whose efficiency is 45% takes heat from a source maintained at a temperature of 327°C. To have an engine of efficiency 60% what must be the intake temperature for the same exhaust (sink) temperature?

What is meant by periodic and nonperiodic motion? Give any two examples, for each motion.

How does the frequency of a tunning fork change, when the temperature is increased?

The radius of gold nucleus is 41.3 fermi. Express its volume in m³.

Two vectors \(\vec A\) and \(\vec B\) of magnitude 5 units and 7 units make an angle 60° with each other. Find the magnitude of the difference vector \(\vec A\) - \(\vec B\) and its direction with respect to the vector \(\vec A\).

What are inertial frames?

After perfectly inelastic collision between two identical particles moving with same speed in different directions, the speed of the particles become half the initial speed. Find the angle between the two before collision.

Why the speed of whirl wind in a Tornado is alarmingly high?

The time period of the satellite of the earth is Sh. If the separation between the earth and the satellite is increased to 4 times the previous value, then what will be the new time period of the satellite acceleration to Kepler's law of periods.

Define cyclic processes

Give the kinetic interpretation of temperature.

Consider two organ pipes of same length in which one organ pipe is closed and another organ pipe is open. If the fundamental frequency of closed pipe is 250 Hz. Calculate the fundamental frequency of the open pipe.

(i) Explain the use of screw gauge and vernier caliper in measuring smaller distances.
(ii) Write a note on triangulation method and radar method to measure larger distances

A projectile is fired horizontally with a velocity u. Obtain the expression for resultant velocity of the projectile at any instant.

Calculate the centripetal acceleration of Moon towards the Earth.

If a particle elastically collides obliquely with a particle of same mass at rest then show that they move perpendicular to each other after collision.

A car of mass 1200 kg is travelling around a circular path of radius 300 m with a constant speed of 54 km/h. Calculate its angular momentum.

Explain how Newton arrived at his law of gravitation from Kepler’s third law.

State and prove Bernoulli’s theorem for a flow of incompressible, non-viscous, and streamlined flow of fluid.

Draw the PV diagram for
a. Isothermal process
b. Adiabatic process
c. isobaric process
d. Isochoric process

From a certain apparatus, the diffusion rate of hydrogen has an average value of 28.7 cm³/s, The diffusion of another gas under the same condition is measured to have an average rate of 7.2 cm³/s. Identify the gas.

Calculate the equivalent spring constant for the following systems and also compute if all the spring constants are equal: