The distance of venus from sun 1.082 x 10¹¹ is and its period of revolutions is 244.633 days. If the period of revolution of the earth around the sun is 365.247 days. Calculate the distance from the sun.

Two billiard balls each of mass 0.5 kg moving in opposite directions with speed 6 m/s collide and rebound with the same speed. What is the impulse imparted to each ball due to the other ?

A solid sphere of radius R made of a material of bulk modulus B is surrounded by a liqiud in a cylindrical container. A massless piston of area  A floats on the surface of the liqiud. When a mass M is placed on the piston on the piston to compress the liqiud, find fractiional change in the radius of the sphere?

A block floats in water and this system is placed in an elevator. If the elevator starts accelerating downwards, will the block float with higher or lower immersed part in the water?

Figure shows momentum versus time graph for a particle moving along x-axis. In which region, force on the particle is large. Why?

Assume that if the shear stress in steel exceeds about 4 x 10⁸N/m² , the steel ruptures. Determine the shearing force necessary to (a) shear a steel bolt 1.00 cm in diameter and (b) punch a 1 cm diameter hole in a steel plate 0.5000 cm thick.

A clock with an iron pendulum keeps correct time at 20^o C. How much will it lose or gain per day, if temperature changes to 40^o C? Coefficient of cubical expansion of iron is 36 x 10^-6 OC^-1 .

A simple harmonic motion has an amplitude A and time period T. What is the time taken to travel from x = A to x = \(\frac{A}{2}\)?

It is a common observation that rain clouds can be at about a kilometre altitude above the ground.
(a) If a rain drop falls from such a height freely under gravity, what will be its speed?Also, calculate in km/h (g = 10 m/s²).
(b) A typical rain drop is about 4 mm diameter.Momentum is mass x speed in magnitude.Estimate its momentum when it hits ground.
(c) Estimate time required to flatten the drop.
(d) Rate of change of momentum is force.Estimate how much force such a drop would exert on you?
(e) Estimate the order of magnitude force on umbrella. Typical lateral separation between two rain drops is 5cm.

trolley of mass 20 kg rests on a horizontal surface. A massless string tied to the trolley passes over a frictionless pulley and a load of 5 kg is suspended from the end of string. If coefficient of kinetic friction between trolley and surface be 0.1, find the acceleration of trolley and tension in the string. ( take g = 10 ms^-2 )

A child running a temperature of 101°F is given an antipyrin (i.e. a medicine that lowers fever) which causes an increase in the rate of evaporation of sweat from his body. If the fever is brought down to 98 °F in 20 minutes, what is the average rate of extra evaporation caused, by the drug. Assume the evaporation mechanism to be the only way by which heat is lost. The mass of the child is 30 kg. The specific heat of human body is approximately the same as that of water, and latent heat of evaporation of water at that temperature is about 580 cal g^-1

Two tuning forks A and B give 5 beats. A resounds with a closed column of air 15 cm long and B with an open column of ar 30.5 cm long. Caluculate their frequencies. Negelct and correction.

A foreigner arrived at Mumbai airport at around 1AM in the moring . She found a text waiting outside. She asked the driver to drop her at the nearby hotel. The taxi driver obliged and drove the foreigner round and round in the city and dropped her at a hotel at around 1:30AM in the morning.
The hotel was only few kilometer away but he charged her one thousand rupees. While driver was arguing with foreigner , a man from the hotel came out to help her. When he heard that drive was charging one thousand rupees, he scolded him and asked him to charge genuinely and not to spoil their country's name. Driver apologised to foreigner and refunded her eight hundred rupees.
The hotel of the foreigner was at a distance of 10 km away from airport on a straight road and dishonest cabman took her along a circuitous path 23 km long and reached the hotel in 28 min. What was the average speed and magnitude of average velocity?

At a point above the surface of the earth, the gravitational potential is \(-5.12\times { 10 }^{ 7 }\ J/kg\) and the acceleration due to gravituy is 0.4 m/s² .Assuming the mean radius of the earth to be 6400 km, calculate the height of the point above the earth's surface.

The difference between the two specific heat capacities (at constant pressure and volume) of a gas is 5000 J kg^-1 k^-1 and the ratio of these specific heat capacities is 1.6. Find the two specific heat capacities i.e. C_p and C_v.

What is the average distance between atoms (interatomic distance) in water? Use the data given in Examples : (i) The density of water is 1000 kgm^-3. The density of water vapour at 100⁰C and 1 atm pressure is 0.6 kgm ^-3 .The volume of a molecule multiplied by the total number gives ,what is called, molecular volume. Estimate the ratio (or fraction) of the molecular volume to the total volume occupied by the water vapour under the above conditions of temperature and pressure.
(ii) Estimate the volume of a water molecule using the data in Example : The density of water is 1000 kgm^-3. The density of water vapour at 100⁰C and 1 atm pressure is 0.6 kgm ^-3 .The volume of a molecule multiplied by the total number gives ,what is called, molecular volume. Estimate the ratio (or fraction) of the molecular volume to the total volume occupied by the water vapour under the above conditions of temperature and pressure.