Who proposed the wave theory?

The dimensions of entropy are

The displacement x of a particle varies with time according to the relation x=\(\frac { a }{ b } \)(1-e^-bt). Then

A particle moves on a given line with a constant speed \(\upsilon \). At a certain time it is at a point P on its straight line path. O is fixed point. The value of \(\overrightarrow { OP } \times \overrightarrow { \upsilon } \) is (where y is perpendicular distance from O to given line)

A particle of mass 5 kg is pulled along a smooth horizontal surface by a horizontal string.
The acceleration of the particle is 10 ms^-2. The tension in the string is

A body is moving unidirectionally under the influence of a source of constant power. Its displacement in time t is proportional to

A man of mass M is standing at the centre of a rotating turn table rotating with an angular velocity w. The man holds two 'dumb bells' of mass M/4 each in each of his two hands. If he stretches his arms to a horizontal position, the turn table acquires a new angular velocity w' where

If three uniform spheres, each having mass M and radius r, are kept in such a way that each touches the other two, the magnitude of the gravitational force on any sphere due to the other two is

Dimensional formula of stress is same as that of

A cylindrical vessel is filled with water upto height H. A hole is bored in the wall at a depth h from the free surface of water. For maximum range, h is equal to

The top of a lake gets frozen at a place where the surrounding air is at a temperature of - 20°C. Then

A black body is at 727°C. It emits energy at a rate which is proportional to

Oxygen and hydrogen gases are at the same temperature T. The kinetic energy of an oxygen molecule will be equal to

A particle executes simple harmonic motion between x = - A and x = + A. The time taken for it to go from 0 to \(A\over 2\) is T₁ and to go from \(A\over 2\) to A is T₂. Then

A source X of unknown frequency produces 8 beats per second with a source of 250 Hz and 12 beats per second with a source of 270 Hz. The frequency of the source X is

What is unified field theory?

How many metric tons are there in teragram?

A particle mover from one postion to another position to the left of the origin in a straight line. Can the displacement of a particle be positive? Explain

What is the minimum number of coplanar vectors of different magnitudes, which may give zero resultant?

A retarding force is applied to stop a motor car. If the speed of the motor car is doubled, how much more distance will it cover before stopping under the same retarding force?

A mass 'm' collides with another mass '2m' and sticks to it. What is the nature of the collision?

Which component of a force does not contribute towards torque

Determine the speed with which the earth would have to rotate on its axis so that a person on the equator would weigh 3/5th as much as at present. Take the equatorial radius as 6400km.

How is compressibility related to bulk modulus?

Two soap bubble of radii 6 cm and 8 cm coalesce to from a single bubble. Find the radius of the new bubble

How does density of a solid change as it is heated ?

A sample of an ideal gas in a cylinder is compressed adiabatically to 1/3 rd of its volume. Will the final pressure be more or less titan 3 times the initial pressure

What will be the internal energy of 8g of oxygen at STP?

The amplitude of a harmonic oscillator is doubled. How does its energy change?

When a source moves at a speed greater than that of sound, will Doppler formula hold? What will happen?

Write in about 1000 words, a fiction piece based on your speculation on the science and technology of the twenty second century.

Rule out or accept the following formula of kinetic energy on the basis of dimensional arguments.
\(R=\frac { 3 }{ 16 } { mv }^{ 2 }\)

To what height does the ball rise and after how long does the ball return to the player's hands?(Take g=9.8ms^-2 and neglect air resistance)

In a harbour, wind is blowing at the speed of 72 km/h and the flag on the mast of a boat anchored in the harbour flutters along the N-E direction. If the boat starts moving at a speed of 51 km/h to the North, what is the direction of flag on the mast of the boat?

A helicopter of mass 1000 kg reises with a vertical acceleration of 15m /s². The crew and the passengers weigh 300 kg. Give the magnitude and direction of the
(i)force on floor by the crew and passengers.
(ii) action of the rotor of the helicopter on the surrounding air
(iii) force on the helicopter due to the surrounding air, take g = 10 m/s².

The blades of a windmill sweep out a circle of area A. (a) If the wind flows at a velocity v perpendicular to the circle, uhat is the mass of the air passing through it in time t? (b) What is the kinetic energy of the air? (c) Assume that the windmill converts 25% of the wind's energy into electrical energy, and that A = 30 m², v = 36 km/h and the density of air is 1.2 kg m^-3. What is the electrical power produced?

Show that for an isolated system the centre of mass moves with a uniform velocity along a straight line path.

A saturn year is 29.5 times the earth year. How far the saturn from the sun of the earth is 1.50x10⁸ km away from the sun?

Why a hollow shaft is stronger than a solid shaft made from the same and equal amounts of material?

What is the largest average velocity of blood flow in an artery of radius 2 \(\times\) 10^{- 3}m, if the flow must remain laminar?

The triple points of neon and carbon dioxide are 24.57 k and 216.55 k, respectively. Express these temperature on the celsius and fahrenheit scales.

A Carnot engine absorbs 6 X 10⁵ cal at 227 ^o C. Calculate work done per cycle by the engine if its sink is maintained at 127^o C.

Calculate (i) r.m.s. velocity (ii) mean kinetic energy of one gram molecule of hydrogen at S.T.P. Given density of hydrogen at S. T.P. is 0.09 kg m^-3.

Obtain an expression for the velocity of  a particle executing SHM, when is this velocity
(ii) minimum

The following equation represents standing wave set up in medium, \(y=4 cos \frac{\pi}{3} sin 40 \ \pi t\) where x and y are in cm and t in sec. Find out the amplitude and the velocity of the two component waves and calculate the distance between adjacent nodes. What is the velocity of a medium particle at x=3 cm 
at time \(\frac{1}{8}\) sec? 

Write down the number of significant figure in the following.
0.04

A scooter is moving along a straight line AB covers a distance of 360 m in 24 s and returns back from B to Cand coveres 240 m in 18 s Find the total path length t.avelled by the scooter

From a school, a group of boys went for a picnic in a village. They went through fields and enjoyed the beauty of nature. While walking, they saw a well which they had never seen in the city. They were very excited and started drawing water from well. They planned to have a competition in which they decide that the who would draw more water would become winner . A villager who was listening to them, went to them and told them about the importance of water. He also explained that they use the water of this for irrigating their fields and also for drinking.
If the two boys raising the bucket, pull it an angle \(\theta \) to each other and each exerts a force of 20N, their effective pull is 30N. What is the angle between their arms?

'A hockey puck with a mass of 0.3 kg slides on the 1 N = 105 dyne C1 horizontal frictionless surface of an ice rink. Two forces act on the puck as shown in figure. The force F₁ has a magnitude of 5 Nand F₂ has a magnitude of 8 N. Determine the acceleration of the puck.

Rohit and Suresh were going to the market when they spotted aman whi left a black bag in the correct of a stall and ran away.They went near it and heard some ticking sound coming form it. They immediately called police and altered the people nearby. By their alertness, a major tragedy was averted.
(i) What qualities of Rohit and Suresh do you appreciate?

Centre of gravity of a body on the earth coincides with its centre of mass for a small object and for a large object, it may not.
What is the qualiative meaning of small and large in this regards? For which following two of them coincides, a building, a pond, a lake, a mountain.

Rajeev was going through Kepler's law of planetary motion. He read that while studying the theory of planetary motion, Kepler established three laws. According to Kepler's second law, the line joining a planet to the sun sweeps out equal areas in equal intervals of time, i.e. the areal velocity of the planet around the sun is constant. This led him to conclude that the linear speed of the planet when closer to the sun is more that its linear speed when away from the sun.
Read the above passage and answer the question.
What values of life do Rajeev learn from Kepler's second law?

Flying tackle
A man carrying mass M = 125 kg makes a flying tackle at v₁ = 4 m/s on a stationary quarterback of mass m =85 kg and his helmet makes solid contact with quarterback's femur.
(ii) If area of cross-section of quarterback's femur is 5 x 10^-4 m², then estimate the shear stress exerted on femur in the collision.

Sahil was going to his friends' house to give him Diwali gift on his motorcycle. He was going at a speed of 60 Km/h. When he saw the red light, he applied the brakes but a car which was behind him, coming at a very high speed, could not stop in time and hit a scooter coming from a side and ran away.
Sahil saw that accident and immediately ran to help the person on scooter. He was bleeding profusely. Sahil stopped an autorikshaw and took the accident victim said that since lot of blood is lost, he had to be given a blood transfusion. 
Sahil immediately offered to donate blood and save a life.
What values of Sahil do you appreciate?

Aman went for a weekend trip with his parents and grandparents to a remote village. His grandfather showed him the fields and the crops they grow. As they moved forward, they saw that a bullock cart got struck in wet mud and the driver was not able to push it out by himself. Seeing him in distress, Aman ran to his help and together they pushed it out, but iron rim of the wheel came out.
They tried to put it on the wheel but it was smaller than diameter of wheel. Suddenly, he got an idea. He collected some wood and set them on fire and heated the rim and then rim easily slipped on the wheel. Cartman thanked Aman and moved away.
What values of Aman does the incident show?

The quantities in the following table represent four different paths for same initial and final states.Find the values a,b,c,d,e,f and g.

What is law of equipartition of energy? Given Avogadro number = 6.02 x 10²³ and Boltzmann's
constant = 1.38 x 10^-23 joule/(molecule-K). Calculate (a) the average kinetic energy of translation
of an oxygen molecule at 27°C, (b) the total kinetic energy of an oxygen molecule at 27°C (c) the
total kinetic energy in joules of a gram-molecule of oxygen at 27°C.

A body of mass 0.2 kg and velocity with 1 s after it passes through it, mean position be 6 m/s executes SHM. Find out the total energy and potential energy of the body if time period of the body is 8s during the SHM?

Namita was writing at the platform along with his uncle for Rajdhani express. Soon she saw the train coming towards the platform. She noticed that as the train was approaching her, the pitch of its whistle appeared to rise and it suddenly appeared to rise and it suddenly appeared to drop as the engine moved away from her.
When the train stopped. Namita and her uncle entered the train. Namita discussed this observation with her uncle. Her uncle, being a Physics teacher, explained her the reason for the change in pitch of the whistle.
(i) What are the value being displayed by Namita?
(ii) Name of the effect involved in the above observation. State this effect briefly.

Explain the relation among Physics, technology and society.

Which of the following is the most precise device for measuring length?
i) A vernier callipers with 20 divisions on the sliding scale.
ii) A screw gauge of pitch 1 mm and 100 divisions on the circular scale.
iii) An optical instrument that can be measure length to within a wavelength of light.

A particle located at x = 0 at time t = 0 starts moving along the positive x direction with a velocity v that varies as v=\(\alpha\sqrt{x}\) . How do the displacement, velocity and acceleration of the particle vary with time? What is the average velocity of the particle over the first s metres of its path?

A particle is projected in air at an angle \(\beta \) to a surface which itself is inclined at an angle \(\alpha \) to the horizontal as shown in figure
Find (i) time of flight (ii) expression for the range on the plane surface i.e. L and (iii) the value of \(\beta \) at which range will be maximum.

Explain why?
It is easier to pull a lawn mower than to push it.

The sign of work done by a force on a body is important to understand .State carefully if the following quantities are positive or negative
Work done by an applied force on a body moving on a rough horizontal plane with uniform velocity

Define radius of gyration and give the physical significance of moment of inertia

Two satellites S₁ and S₂ revolve round a planet in coplanar circular orbit in the same sense. Their periods of revolution are one hour and 8 hours respectively. The radius of the orbit of S₁ is 10⁴ km. When S₂ is close to S₁ find
(i) the speed of S₂ relative to S₁
(ii) the angular speed of S₂ as actually observed by an astronaut in S₁.

What do you understand by Poisson's ratio? Find the value of Poisson's ratio at which the volume of a wire does not change when the wire is subjected to a tension.

Explain why
(a) The angle of contact of mercury with glass is obtuse, while that of water with glass is acute.
(b) Water on a clean glass surface tends to spread out while mercury on the same surface tends to form drops. (Put differently, water wets glass while mercury does not.)
(c) Surface tension of a liquid is independent of the area of the surface.
(d) Water with detergent dissolved in it should have small angles of contact.
(e) A drop of liquid under no external forces is always spherical in shape.

Wlzat is Calorimetry? State its principle
A copper calorimeter of mass 100 g contains 200 g of a mixture of ice and water. Steam at 100⁰C under normal pressure is passed into the calorimeter and the temperature of the mixture is allowed to rise to 50°C. If the mass of the calorimeter and its contents is now 330 g, what was the ratio of ice and water in the beginning? Neglect heat losses. Given
Specific heat capacity of copper = 0.42 x 10³ J Kg^-1k^-1
Specific heat capacity of water = 4.2 x 10³ J Kg^-1K^-1
Latent heat affusion of ice = 3.36 x 10⁵ J kg-1
Latent heat of condensation of steam = 22.5 x 10⁵ J kg-1

Heat cannot flow itself from a body at lower temperature to a body at higher temperature, is a consequence of which law of thermodynamics?

Consider an ideal gas with following  distribution of speeds.

(i) Calculate V_rms and hence \(T(m=3.0\times { 10 }^{ -26 }kg)\)
(ii) If all the molecules with speed 1000 m/s escape from the system, calculate new V_rms and hence T. 

The motion of a particle executing simple harmonic motion is described by the displacement function.
x(t) = A cos (ωt + \(\phi \))
If the initial (t = 0) position of the particle is I em and its initial velocity is ω cm/s, what are its amplitude and initial phase angle? The angular frequency of the particle is \(\pi\)s^-1. If instead of the cosine junction, we choose the sine junction to describe the SHM: x = B sin (ພt + α), what are the amplitude and initial phase of the particle with the above initial conditions?

A whistle of frequency 540 Hz rotates in a circle of radius 2 m at a linear speed of 30 m/s. What is the lowest and highest frequency heard by an observer along distance away at rest with respect to the centre of circle. Take speed of sound in air as 330 m/s. Can the appartment frequency be ever equal to actual?