The velocity of a particle v at an instant t is given by v = at + br². The dimensions of b is

If the velocity is \(\overrightarrow { v } =2\hat { i } +{ t }^{ 2 }\hat { j } -9\overrightarrow { k } \), then the magnitude of acceleration at t = 0.5s is

\(\vec A\times \vec B\) is ____________.

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

A spring of force constant k is cut into two pieces such that one piece is double the length of the other. Then, the long piece will have a force constant of

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

Moment of inertia of a this uniform hollow cylinder about an axis passing perpendicular to the length and passing through the center is _____________.

If the distance between the Earth and Sun were to be doubled from its present value, the number of days in a year would be

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

A parrot sitting on the floor of a wire cage which is carried by a boy, starts flying the boy will feel that the box is now _____________.

A distant star emits radiation with maximum intensity at 350 nm. The temperature of the star is

The following graph represents the pressure versus number density for ideal gas at two different temperatures T₁ and T₂. The graph implies

A hollow sphere is filled with water. It is hung by a long thread. As the water flows out of a hole at the bottom, the period of oscillation will

A spring balance has a scale that reads from o to 50 kg the length of the scale is 20 cm. A body suspended from this balance, when displaced and released, oscillates with a period of 0.6 s. Then the weight of the body will be ______________.

An organ pipe A closed at one end is allowed to vibrate in its first harmonic and another pipe B open at both ends is allowed to vibrate in its third harmonic. Both A and B are in resonance with a given tuning fork. The ratio of the length of A and B is

State the number of significant figures in 0.2300m

Is it possible to measure the depth of a well using kinematic equations?

The momentum of a system of particles is always conserved. True or false?

Why a metal ball rebounds better than a rubber ball?

A force of \((4\hat{i}-3\hat{j}+5\hat{k})\) N is applied at a point whose position vector is \((7\hat{i}+4\hat{j}-2\hat{k})\) m. Find the torque of force about the origin.

Distinguish between cohesive and adhesive forces.

What is Wien’s law?

Write short notes on two springs connected in series.

Two astronauts on the surface of the moon cannot talk to each other why

What are fundamental units and derived units?

What is the difference between velocity and average 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?

20 J work is required to stretch a spring through 0.1 m. Find the force constant of the spring. If the spring is further stretched through 0.1 m, calculate work done.

Write an expression for Cartesian co-ordinates of the CM for uniform distribution of mass.

A particle is projected upward from the surface of the earth (radius) with a K.E equal to half the minimum value needed for it to escape. To which height, does it rise above the surface of earth?

What is meant by triple point? Give the values of triple point pressure & triple point temperature of water.

In the upper part of the atmosphere the kinectic temperature of air is of the order of 1000 K, even then one feels severe cold there. Why?

Consider a tuning fork which is used to produce resonance in an air column. A resonance air column is a glass tube whose length can be adjusted by a variable piston. At room temperature, the two successive resonances observed are at 20 cm and 85 cm of the column length. If the frequency of the length is 256 Hz, compute the velocity of the sound in air at room temperature.

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)

Mention important properties of the scalar product of two vectors.

The Moon orbits the Earth once in 27.3 days in an almost circular orbit. Calculate the centripetal acceleration experienced by the Earth? (Radius of the Earth is 6.4\(\times\)10⁶ m).

What is meant by elastic potential energy? Drive an expression for the elastic potential energy of the spring.

Calculate the work done by the torque.

Derive an expression for escape speed.

Derive an equation for the total pressure at a depth ‘h’ below the liquid surface.

Explain in detail the isochoric process.

Derive Meyer's relation.

Discuss in detail the energy in simple harmonic motion.