Write the rules for determining significant figures.

How many parallactic second are there in one Astronomical unit?
Given data:
1 parallactic second = 3.08\(\times\)10¹⁶m
1 Astronomical unit = 1.496\(\times\)10¹¹m

Calculate the number of times a human heart beats in the life of 100 years old man. Time of one heart beat = 0.8s.

A bullet going with speed 350 m/s enters in a concrete wall and penetrates a distance of 5 cm before coming to rest. Find the deceleration.

Two vectors \(\vec A\) and \(\vec B\) are given in the component form as \(\overrightarrow { A } =5\hat { i } +7\hat { j } -4\hat { k } \) and \(\overrightarrow { B } =6\hat { i } +3\hat { j } +2\hat { k } \). Find \(\vec { A } +\vec { B } ,\vec { B } +\vec { A } ,\vec { A } -\vec { B } ,\vec { B } -\vec { A } \)

Consider an object travelling in a semi-circular path from point O to point P in 5 second, as is shown in the Figure. Calculate the average velocity and average speed.

Explain the meaning of law of conservation of linear momentum.

A block of mass m is pushed momentarily along a horizontal surface with an initial velocity u. If u_k is the coefficient of kinetic friction between the object and surface, find the time at which the block comes to rest.

What is mechanical energy? What are its two types?

A rope of negligible mass is wound round a hollow cylinder of mass 3 kg and radius 40 cm. What is angular acceleration of the cylinder if the rope is pulled with a force of 30N? What is the linear acceleration of the rope? Assume that there is no slipping.

A jester in a circus is standing with his arms extended on a turn table rotating with angular velocity \(\omega\). He brings his arms closer to his body so that his moment of inertia is reduced to one third of the original value. Find his new angular velocity. [Given: There is no external torque on the turn table in the given situation.] 

Draw graphs showing the variation of acceleration due to gravity with
(i) height above the earth's surface
(ii) depth below the earth's surface.

A body floats in water with 40% of its volume outside water. When the same body floats in oil 60% of its volume, remains outside oil. What is the relative density of the oil?

The temperature - entropy diagram of a reversible engine cycle is given in figure. Calculate its efficiency.

If the length of the simple pendulum is increased by 44% from its original length, calculate the percentage increase in time period of the pendulum.

Alcohol in a U tube executes S.H.M of time period T. Now, alcohol is replaced by water upto the same height in the U-tube. What will be the effect on the time period?

Derive the expression for resultant spring constant when two springs having constant k₁ and k₂ are connected in series.

Describe the formation of beats.

Write about the formation of waves in a tuning fork.

How are sound waves-classified?