The range of strong nuclear force is about

The density of a cube is measured by measuring its mass and the length of its sides. If the maximum errors in the measurement of mass and length are 3% and 2% respectively, then the maximum error in the measurement of density is _____.

In case of a moving body

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)

An insect is crawling up on the concave surface of a fixed hemispherical bowl of radius R. If the coefficient of friction is \({1\over3}\) then the height up to which the insect can crawl is nearly,_______.

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

A loaded spring gun of mass M fires a 'shot' of mass m with a velocity \(\vartheta \) at an angle of elevation \(\theta\). The gun is initially at rest on a horizontal frictionless surface. After firing, the centre of mass of the gun-shot system

If g is the acceleration due to gravity on the earth's surface, the gain in the potential energy of an object of mass m raised from the earth's surface to a height equal to the radius R of the earth,is

Young's modulus of a material has the same unit as

Two small drops of mercury, each of radius R, coalesce to form a single large drop. The ratio of the total surface energies before and after the change is:

The scale on a steel meter rod is calibrated at 20°C. What will be the error in the reading of 50 ern at 27°C? Take, a = 1.2 x 10.5 °C^-1

The S.l. unit of mechanical equivelent of heat is _______.

According to kinetic theory of gases the r.m.s. velocity of the gas molecules is directly proportional to

A heavy brass sphere is hung from a spring and it executes vertical vibrations with period T. The sphere is now immersed in a non-viscous liquid with a density (1/10)^th that of brass. When set into vertical vibrations with the sphere remaining inside liquid all the time, the time period will be

An empty vessel is partially filled with water. The frequency of vibration of air column in the vessel

The industrial revolution in England and Western Europe more than two centuries ago was triggered by some key scientific and technological advances. What were these advances?

A famous relation in physics relates ‘moving mass’ m to the ‘rest mass’ m_o of a particle in terms of its speed v and the speed of light, c. (This relation first arose as a consequence of special relativity due to Albert Einstein). A boy recalls the relation almost correctly but forgets where to put the constant c. He writes :  \(m=\frac { { m }_{ 0 } }{ (1-{ \nu }^{ 2 })^{ 1/2 } } \). Guess where to put the missing c.

Can a body be said to be rest as well as in motion at the same time.How?

A boy can jump on the moon six times as high as on the earth. Why?

What is the angle between frictional force and instantaneous velocity of the body moving over a rough surface?

What should be the angle between the force and the displacement for maximum and minimum work?

Two satellites of equal masses are orbiting at different heights. Will their moments of inertia be the same or different?

A satellite revolving around earth loses height. How will its time period be changed?

What is the shape of stress-strain graph within elastic limit?

In deriving Bernoulli's equation, we equated the work done on the fluid in the tube to its change in the potential and kinetic energy.
Do the dissipative forces become more important as the fluid velocity increases? Discuss qualitatively.

What is the condition for the difference between the length of a certain brass rod and that of a steel rod to be constant at all temperature?

Which one among a solid, liquid and gas of the same mass and at the same temperature has the greatest internal energy and which one has the least?

A gas is contained in a closed vessel. How pressure due to the gas will be affected if force of attraction between the molecules disseppear sudenly?

What will be the time period of oscillation, if the length of a second pendulum is one third?

In a longitudinal wave, what is the distance between a compression and its nearest rarefraction ?

Briefly explain how physics is related to technology.

Compute the following with regards to significant figures.
(i) \(4.6\times 0.128\).
(ii) \(\frac { 0.9995\times 1.53 }{ 1.592 } \).
(iii) 876 + 0.4382.

Draw positiontime graph for Positive velocity

The ceiling of a long hall is 25 m high. What is the maximum horizontal distance that a ball thrown with a speed of 40 m s-1 can go without hitting the ceiling of the hall ?

A helicopter of mass 500 kg rises with a vertical acceleration of 10 ms^-2. The weight of pilot is 60 kg. Give the magnitude and direction of
(i) force on the floor of the helicopter by the pilot
(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 ms^-2).

Draw a graph showing variation of potential energy, kinetic energy and the total energy of a body freely falling on Earth from a height h.

In the HCl molecule, the separation between the nuclei of the two atoms is about 1.27 Å (1 Å = 10^-10 m). Find the approximate location of the CM of the molecule, given that a chlorine atom is about 35.5 times as massive as a hydrogen atom and nearly all the mass of an atom is concentrated in its nucleus.

The distances of two planets from the sun are 10¹³ m and 10¹² m, respectively. Calculate the ratio of time period and the speeds of the two planets

Read the following two statements below carefully and state, with reasons, if it is true or false.
(a) The Young’s modulus of rubber is greater than that of steel;
(b) The stretching of a coil is determined by its shear modulus.

The flow rate of water from a tap of diameter 1.25 cm is 0.48 L/min. The coefficient of viscosity of water is 1O^-3Pa-s. After some time the flow rate is increased to 3 L / min. Characterize the flow for both the flow rates.

When 0.2 kg of a body at 100°C is dropped into 0..5 kg of water at 10°C, the resulting temperature is 16°C. Find the specific heat of the body. Specific heat of water is 4.2 x 10³ J/kg/⁰c.

Explain why
(a) Two bodies at different temperatures T₁ and T₂ if brought in thermal contact do not necessarily settle to the mean temperature (T₁ + T₂ )/2.
(b) 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.
(c) Air pressure in a car tyre increases during driving. (d) The climate of a harbour town is more temperate than that of a town in a desert at the same latitude.

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.

Answer the following question
(i) Time period of a particle in SHM depends on the force constant k and miss m of the particle \({ T }=2\pi \sqrt { \frac { m }{ k } } \). A simple pendulum executes SHM approximately. Then why is the time period of a pendulum independent of the mass of the pendulum?
(ii) The motion of a simple pendulum is approximately simple harmonic for small angle oscillations. For larger angles of oscillation, a more involved analysis shows that T is greater than \(2\pi \sqrt { \frac { l }{ g } } \) .Think of a qualitative argument to appreciate this result.
(iii) A man with a wristwatch on his hand falls from the top of a tower. Does the watch give correct time during the free fall?
(iv) What is the frequency of oscillation of a simple pendulum mounted in a cabin that is freely falling under gravity?

Earthquakes generate sound waves inside the earth. Unlike a gas, the earth can experience both transverse (S) and longitudinal (P) sound waves. Typically the speed of S wave is about 4.0 km s^–1, and that of P wave is 8.0 km s^–1. A seismograph records P and S waves from an earthquake. The first P wave arrives 4 min before the first S wave. Assuming the waves travel in straight line, at what distance does the earthquake occur?

Miss Rita in her physics class was explaining how to use a vernier calliper to measure small dimension.Her student Anubha was confused that why didn't we used a metre scale for the purpose. She asked we Miss Rita who explained her that a proper instrument and unit should be used to get accurate measurement.Large dimensions such as distance of earth from Sun is measured in light year(ly) whereas size of nucleus is measured in fermi(fm).
What values of Anubha and her teacher do your appreciate?

John and Kuldeep are good friends.Both were driving their bikes.Speed thrill Kuldeep.Suddenly, Kuldeep met an accident.He was injured.When John heard about accident,he reached at the site of the accident and noticed that Kuldeep was lying on the roadside John informed the PCR that was petrolling.Kuldeep was taken to the city hospital,where he was treated by doctors.The speedometer of the bike of Kuldeep was reading 110km/h at the time of accident.
Comment on the attitude of Kuldeep. 

A body of mass 10 kg revolves in a circle of diameter 0.4m making 1000 revolutions per minute. Calculate its linear velocity and centripetal acceleration.

A Force Applied on a sledge
A horizontal force of 980 N is required to slide a sledge weighing 1200 kgf over a flat surface. Calculate the coefficient of friction.

To simulate car accidents, auto manufacturers study the collisions of moving cars with mounted springs of different spring constants. Consider a typical simulation with a car of mass 1000 kg moving with a speed 18.0 km/h on a smooth road and colliding with a horizontally mounted spring of spring constant 5.25 × 10 3 N m^–1 . What is the maximum compression of the spring ?

Find the torque of a force \(7\hat { i } +3\hat { j } -5\hat { k } \) about the origin. The force acts on a particle whose position vector is \(\hat { i } -\hat { j } +\hat { k } \)

Shweta was reading a book on the biography of Issac Newton. She read that Newton was sitting under an apple tree when a falling apple led him to develop a whole new science of gravity. After reading the book, shweta realised that every phenomenon in universe has some scientific fact associated with it, it depends on us whether we look for a scientific fact or associate a superstition with it.
How can you find the mass of the earth using law of gravitation?

Ajay was a very naughty boy. One day , he bought a rubber cord catapult from market and started hitting passerby . When his father came to know about this, he immediately called Ajay and scolled him. He made him realise what damage his act could do. Ajay realised his mistake and apologised for his mistake.
  A rubber cord catapult a cross-section area of 1mm² and total unstreched length 10cm. It is stretched to 12 cm and then released to project a missile of mass 5g. Taking Young's modulus for rubber as 5.0x10⁸Nm^-2 , find the tension in the cord,Also, find the velocity of projection of the projectile.

Two syringes of different cross-section(without needles) filled with water are connected with a tightly fitted rubber tube.Diameters of the smaller and larger piston are 1.0 cm and 3.0 cm, respectively.
If the smaller piston is pushed in through 6.0 cm, how much does the larger piston move out?

Melwin  found that his friend suffering from fever. He took him to the doctor for treatment. The doctor kept the thermometer in the mouth of the patient to noted the reading. The reading shown by thermometer was 102 F. 
Doctor gave the necessary medicine to Melwin friends.
What is value of temperature in celsius?

A Carnot engine whose heat sink is at 27°C has an efficiency of 40%. By how many degrees should the temperature of source be changed to increase the efficiency by 10% of the original efficiency?

 A Lawn Roller 
A lawn roller has been pushed by a gardener through a distance of 30 m. What will be the work done by him if he applies a force of 30 kg -wt in the direction inclined at 60^o to the ground? Take g = 10 m/s²

A particle set to be in SHM having two types of energies, potential and kinetic. The potential energy is on account of displacement of the particle from the mean position and kinetic energy is on account of the velocity of the particle. At any instant of time t, these are
\(PE=U=\frac { 1 }{ 2 } m{ \omega }^{ 2 }{ x }^{ 2 }=\frac { 1 }{ 2 } { m\omega }^{ 2 }{ A }^{ 2 }{ sin }^{ 2 }\omega t\)
\(\\ KE=K=\frac { 1 }{ 2 } m{ \omega }^{ 2 }({ A }^{ 2 }-{ x }^{ 2 })=m{ \omega }^{ 2 }{ A }^{ 2 }{ cos }^{ 2 }\omega t\)
and TE = PE + KE = \(\frac { 1 }{ 2 } m{ \omega }^{ 2 }{ A }^{ 2 }\)  = Constant where, m = mass of the particle
(a) At what distance from the mean position ( a fixed point) will KE of the particle would be twice of its PE?
(b) What are the applications of this study in our day-to-day life?

Two waves of equal frequencies have their amplitudes in the ration of 3:5. They are superimposed on each other.Calculate the ratio of I_max/I_min.

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.

It is required to find the volume of a rectangular block. A Vernier Caliper is used to measure the length, width and height of the block. The measured values are found to be 1.37 cm, 4.11 cm and 2.56 cm respectively.

How does the velocity-time graph for uniform motion give a geometrical way of calculating the displacement covered during a given time t?

A particle is thrown over a triangle from one end of a horizontal base that grazing the vertex falls on the other end of the base, If \(\alpha \quad and\quad \beta \) be the base angles and \(\theta \) be the angle of projection, then show that \(\tan { \theta } =\tan { \alpha } +\tan { \beta } \)

A hammer weighing 1 kg moving with the speed of 20 m / s strikes the head of a nail driving it 20 cm into a wall. Neglecting the mass of the nail, calculate
(i) the acceleration during the impact
(ii) the time interval during the impact
(iii) the impulse.

Two particles A and B of masses m and 2m, are moving along the X and Y-axes, respectively with the same speed of v. They collide at the origin and coalesce into one body after the collision. What is the velocity of the coulesced mass? What is the loss of energy during this collission?

A metre stick is balanced on a knife edge at its centre. When two coins, each of mass 5 g are put one on top of the other at the 12.0 cm mark, the stick is found to be balanced at 45.0 cm. What is the mass of the metre stick?

What do you understand by gravitational field, intensity of gravitational field . Prove that gravitational intensity at a point is equal to the acceleration due to gravity at that point.

Define the following terms:
(i) elastic limit
(ii) elastic fatigue
(iii) breaking stress
A steel wire of cross-sectional area 0.5 mm² is held between two fixed supports. If the tension in the wire is negligible and it is just taut at a temperature of 20°C, determine the tension when the temperature falls to O°C. Young's modulus of steel is 21 x 10¹¹ dyne cm^-2 and the coefficient of linear expansion of steel is 12 x 10^-6 per ⁰C. Assume that the distance between the supports remains unchanged.

A manometer reads the pressure of a gas in an enclosure as shown in Fig. (a). When a pump removes some of the gas, the manometer reads as in Fig. (b). The liquid used in the manometers is mercury and the atmospheric pressure is 76 cm of mercury.
(a) Give the absolute and gauge pressure of the gas in the enclosure for cases (a) and (b), in units of cm of mercury.
(b) How would the levels change in case (b) if 13.6 cm of water (immiscible with mercury) is poured into the right limb of the manometer? Ignore the small change in the volume of the gas.

The coefficient of apparent expansion of a liquid when determined using two different vessels A and Bare \(\gamma\)l and \(\gamma\)2 respectively. If the coefficient of linear expansion of vessel A is a, find the coefficient of linear expansion of vessel B.

Four moles of an ideal gas having \(\gamma \) = 1.67 are mixed with 2 moles of another ideal gas having\(\gamma \)  = 1.4.Find the value of \(\gamma \) for resulting mixture of gases

Suppose a tunnel is dug through the earth from one side to the other side along a diameter. Show that the motion of a particle dropped into the tunnel is simple harmonic motion. Find the time period. Neglect all the frictional forces and assume that the earth has a uniform density. G = 6.67 x 10^-11 Nm² kg^-2; density of earth = 5.51 x 10³ kg m^-3