The range of strong nuclear force is about

A wire has a mass 0.3 ± 0.003 g, radius 0.5 ± 0.005 mill and length 6 ± 0.06 cm. The maximum percentage error in the measurement of its density is _____.

Distance-time graph of a body at rest is

A plane is indined at an angle of 30° with horizontal. The magnitude of component of a vector \(\overset\rightarrow{A}\)=-10\(\hat{k} \) perpendicular to this plane is (here z-direction is vertically upwards

If the tension in the cable supporting an elevator is equal to the weight of the elevator, the elevator may _______.

What is the dimensions of power:

A cylindrical solid of mass M has raidus R and length L. Its moment of inertia about a generator is:

Mars has about 1/10th as much mass as the earth and half as great a diameter. TI1e acceleration of a falling body on Mars is about

Dimensional formula of stress is same as that of

For a ball falling in a liquid with constant velocity, ratio of resistance force due to the liquid to that due to gravity is

An ideal heat engine exhosting heat at 27°C is to have 25%efficiency. It must take heat at: _______.

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

Two particles P and Q describe SHM of same amplitude a and frequency v along the same straight line. The maximum distance between two particles is √2 a. The phase difference between the particles is

Two pulses in a stretched string whose centres are initially 8 cm apart are moving towards each other as shown in figure. The speed of each pulse is 2 cms^-1. After 2 second, the total energy of the pulses will be

What is meant by unification of physical laws?

Which is a bigger unit-light year or parsec?

A passenger arriving in a new town wishes to go from the station to a hotel located 10 km away on a straight road from the station. A dishonest cabman takes him along a circuitous path 23 km long and reaches the hotel in 28 min. What is
(a) the average speed of the taxi,
(b) the magnitude of average velocity ? Are the two equal ?

A man weighing 60 kg is sitting in a lift which is moving vertically with an acceleration of 2 ms^-2. Prove that the reaction on the base of the lift is greater when it is ascending than when it is descending. (Given g = 9.8 ms^-2).

What is the nature of force involved in the winding of a watch?

Is it possible to open a pen cap with one finger? Why?

The acceleration due to gravity on a planet is 1.96\({ ms }^{ -2 }\). If it is safe to jump from a height of 2m on the earth, then what will be the corresponding safe height on the planet?

Name three physical properties which can have different values in different directions.

A vertical off-shore structure is built to withstand a maximum stress of 10⁹ Pa. Is the structure suitable for putting up on top of an oil well in the ocean ? Take the depth of the ocean to be roughly 3 km, and ignore ocean currents.

The difference between length of a certain brass rod and that of a steel rod is claimed to be constant at all temperatures. In this possible?

Two samples of a gas initially at the same temperature and pressure are compressed from a volume V to a volume V/2. One sample is compressed isothermally and the other adiabatically.In which sample is the pressure greater?Justify.

Find the temperature at which rms speed of a gas is half of its value of 0⁰C, pressure remaining constant.

Can a motion be periodic but not oscillatory? If your answer is yes, give an example and if not explain why?

An observer places his ear at the end of a long steel pipe. He can hear two sounds, when a workman hammers the other end of the pipe. Why?

Briefly, do we need quantum theory?

The distance of the Sun from the Earth is 1.496 x 10¹¹ m (i.e., 1 A.u.). If the angular diameter of the Sun is 2000. find the diameter of the Sun.

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)

The acceleration associated with a mass 'm' moving in a circular path is Eobefound. It is given that the velocity at any instant is v = krt, where k is a constant. Classify the motion and find acceleration.

A particle moves in a circle of radius 20 cm. Its linear speed at any time is given by v = 2t where v is in m/s and t is in seconds. Find the radial and tangential accelerations at t = 3 seconds and hence calculate the total acceleration at this time.

A body of mass 2kg is at rest at a height of 10 m above the ground. Calculate its potential energy and kinetic energy after it has fallen through half the height. Also find the velocity at this instant.

prove the relation \(\tau =I\alpha \), for a rigid body rotating about a fixed axis.

A comet orbits the sun in a highly elliptical orbit. Does the comet have a constant
(a) linear speed,
(b) angular speed,
(c) angular momentum,
(d) kinetic energy,
(e) potential energy,
(f) total energy throughout its orbit? Neglect any mass loss of the comet when it comes very close to the Sun.

Determine the force required to double the length of a steel wire of area of cross-section 5 x 10^-5m². Young's modulus of steel  =2 x 10¹¹ Nm^-2.

A small drop of water of surface tension T is squeezed between two clean glass plates so that a thin layer of thickness d and area A is formed between them. If the angle of contact is zero, what is the force required to pull the plates apart.

The brass scale of a barometer gives correct reading at 0 ⁰C. Coefficient of linear expansion of brass is 2.0 x 10^-5/⁰ C. The barometer reads 75.00 cm at 27⁰ C. What is the true atmospheric pressure at 27⁰ C.

Explain, why?
(i) 500 J of work is done on a gas to reduce its volume by compression adiabatically. What is the change in internal energy of the gas?
(ii) The coolant in a chemical or a nuclear plant , i.e. the liquid used to prevent the different parts of a plant from getting too hot should have high specific heat.
(iii) The climate of a harbour town is more temperate than that of a town in a desert at the same latitude

State the assumptions of the kinetic theory of gases. The density of carbon dioxide gas at 0 °C and at a pressure of 1.0 x 10⁵ newton/metre²: is 1.98 kg/m³. Find the root mean square velocity of its molecules at 0 °C and 30°C. Pressure is constant.

The relation between the acceleration a and displacement x of a particle executing SHM is
a = -\(\left( \frac { p }{ q } \right) \)y, where p and q are constants.

A stone dropped from the top of a tower of height 300 m splashes into the water of a pond near the base of the tower. When is the splash heard at the top given that the speed of sound in air is 340 m s^–1 ? (g = 9.8 m s^–2)

Round off the following number as indicated
143.45 upto 4 digits

A cyclist is riding with a speed of 27kmh^-1. As he approaches, a circular turn on the road of f radius 80 m, he applies brakes and reduces his speed at the constant rate of 0.5 ms^-2.What is the magnitude and direction of the net acceleration of the cyclist on the circular turn?

Force on the Block
A block P of mass 4 kg is placed on another block Q of mass 5 kg, and the block Q rests on a smooth horizontal table. For sliding block P on Q, horizontal force of 12 Nis required to be applied on P. How much maximum force can applied on Q so that both P and Q move together? Also, find out acceleration produced by this force.

Mahak was very lazy and overweight.She didn't do any exercise or physical work. As her weight was increasing whenever she walked she felt pain in her knees. She consulted a doctor who advised her to reduce her weight otherwise her condition would not improve. She tried to follow doctors advice and changed her life style, she stopped eating junk food, started using stairs instead of using cars. After sometime, she became fit and fine again.
(i) What values do you infer from this?

To maintain a rotor at a uniform angular speed of 200 rad s^-1, an engine needs to transmit a torque of 180 N m. What is the power required by the engine ? (Note: uniform angular velocity in the absence of friction implies zero torque. In practice, applied torque is needed to counter frictional torque). Assume that the engine is 100% efficient.

The acceleration due to gravity at the moon's surface is 1.67 ms^-2 . If the radius of the moon is 1.74x10⁶ m, then calculate the mass of the moon.

Flying tackla
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.
(i) What is the final speed of two athletes immediately after contact and also determine the average force exerted on the quarterback's femur, when last collision occur at 0.100 s ?
(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.

A Cube Placed in Water and Mercury 
A tank contains water and mercury as shown in figure. An iron cube of edge 6 cm is in equilibrium as shown in figure. What is the fraction of cube inside the mercury? Given, density of iron =- 7.7 x 10³ kqm^-3 and density of mercury =- 13.6 x 10³ kgm^-3

2 A blacksmith fixes iron ring on the rim of the wooden wheel of a horse cart. The diameter of the rim and the iron ring are 5.243 m and 5.231 m, respectively at 27 °C. To what temperature should the ring be heated so as to fit the rim of the wheel?

Write the expressions for Cv and Cp of a gas in terms of gas constant R and constant y, where \(γ={C_P\over C_v}\)

A balloon has 5.0 g mole of helium at 7⁰C Calculate the number of atoms of helium in the balloon.

The vertical motion of a huge piston in machine is simple harmonic with a frequency of 0.50 s^-1. A block of 10 kg is placed on the piston. What is the maximum amplitude of the piston's SHM for the block and the piston to remain together?

Science, like any knowledge, can be put to good or bad use, depending on the user. Given below are some of the application of science. Formulate your views on whether the particular application is good, bad or something that cannot be so clearly categorized.
(i) Mass vaccination against small pox to curb and finally eradicate this disease from the population.
(ii) Television for eradication of illiteracy and for mass communication for news and ideas.
(iii) Prenatal sex determination.
(iv) Computers for increase in work efficiency.
(v) Putting artificial satellites around the earth.
(vi) Development of nuclear weapons.
(vii) Development of new and powerful techniques of chemical and biological warfare.
(viii) Purification of water for drinking.
(ix) Plastic surgery.
(x) Cloning.

Just as precise measurements are necessary in science, it is equally important to be able to make rough estimates of quantities using rudimentary ideas and common observations. Think of ways by which you can estimate the following (where an estimate is difficult to obtain, try to get upper bound on the quantity).
The number of strands of hair on our head

Two stones are thrown up simultaneously from the edge of a cliff 200 m high with initial speeds of 15 ms^-1 and 30 ms^-1, Verify that the graph shown in Fig. correctly represents the time variation of the relative position of the second stone with respect to the first. Neglect air resistance and assume that the stones do not rebound after hitting the ground. Take g = 10 ms>. Give the equations for the linear and curved parts of the plot.

A projectile, launched with a speed v at an angle \(\theta\) to the horizontal, hits a plane inclined at an angle a to the horizontal (\(\alpha < \theta\)) and passing through the point of launching. Obtain an expression for the range r of the projectile on this inclined plane. When does the projectile hit this plane?

Figure shows (x, t), (y, t) diagram of a particle moving in 2-dimensions.
 
If the particle has a mass of 500 g, find the force (direction and magnitude) acting on the particle.

Two 22.7 kg ice sleds A and B are placed a short distance apart, one directly behind the other, as shown in Fig. A 3.63 kg cat, standing on one sled, jumps across to the other and immediately back to the first. Both jumps are made at a speed of 3.05 ms^-1 relative to the ice. Find the final speeds of the two sleds.

Find the centre of mass for a solid cone of base radius r and height h.

The planet Neptune travels around the sun with a period of 165 yr. Show that the radius of its orbit is approximately thirty times that of the earth's orbit, both being considered as circular.

A 14.5 kg mass, fastened to the end of a steel wire of unstretched length 1.0 m, is whirled in a vertical circle with an angular velocity of 2 rev/s at the bottom of the circle. The cross-sectional area of the wire is 0.065 cm² . Calculate the elongation of the wire when the mass is at the lowest point of its path.

If the terminal speed of a sphere of gold (density = 19.5\({ kg }/{ { m }^{ 3 } }\)) is 0.2m/s in viscous liquid (density = 19.5\({ kg }/{ { m }^{ 3 } }\)) is 0.2m/s in viscous liquid density (density = 1.5\({ kg }/{ { m }^{ 3 } }\)). Find out the terminal speed of a sphere of silver(density = 10.5\({ kg }/{ { m }^{ 3 } }\)) of the same size in the same liquid.

The absolute temperature (kelvin scale) T is related to the temperature t_c on the celsius scale by t_c =T-273.15. Why do we have 273.15 in this relation and 273.16?

Estimate the total number of air molecules (inclusive of oxygen, nitrogen, water vapour and other constituents) in a room of capacity 25.0 m³ at a temperature of 27 °C and 1 atm pressure.

Show that for a particle in linear SHM the average kinetic energy over a period of oscillation equals the average potential energy over the same period.