The radius of the circle is 3.12 m. Calculate the area of the circle with regard to significant figures.

Assuming that the frequency \(\gamma\) of a vibrating string may depend upon
(i) applied force (F) 
(ii) length (I)
(ill) mass per unit length (m), prove that \(\gamma\alpha{{1}\over{l}}\sqrt{{{F}\over{m}}}\) using dimensional analysis.

In a series of successive measurements in an experiment, the readings of the period of oscillation of a simple pendulum were found to be 2.63s, 2.56s, 2.42s, 2.71s, and 2.80s.
Calculate
(i) the mean value of the period of oscillation
(ii) the absolute error in each measurement
(iii) the mean absolute error
(iv) the relative error
(v) the percentage error.
(vi) Express the result in proper form.

Two resistances R₁ = (100 ± 3) \(\Omega\), R₂ = (150 ± 2)\(\Omega\), are connected in series. What is their equivalent resistance?

Round off the following numbers as indicated 19.45 up to 3 digits

A object is thrown with initial speed 5 ms^-1 with an angle of projection 30\(\gamma \) . What is the height and range reached by the particle?

A car is moving along X-axis. As shown in figure it moves from O to P in 18 seconds and return from P to Q in 6 second. What are the average velocity and average speed of the car in going from
(I)O to P
(II) From O to P and back to Q

A charged particle moves towards another charged particle. Under what conditions the total momentum and the total energy of the system conserved?

An object of mass m is projected from the ground with initial speed v₀. Find the speed at height h.

Calculate moment of inertia with respect to rotational axis xx' in following figures (a) and (b).

When an object be in mechanical equilibrium?

Why is the energy of a satellite (or any other planet) negative?

State Pascal’s law in fluids.

A wire elongates by Imm when a load w is hanged from it if the wire goes over a pulley and 2 weights w each are hung at the 2 ends, what will be the elongation of wire in mm?

What is sphere of influence?

Define molar specific heat capacities.

For a gas the difference between the two specific heats is 4150 J/Kg K. What is the specific heat of the gas at constant volume if the ratio of specific heat is 1.4?

What are the factors which effect Brownian motion?

If the rms speed of hydrogen molecules at 300 K is 1930 ms^-1. Then what is the rms speed of oxygen molecules at 1200 K.

Compute the time period for the following system if the block of mass m is slightly displaced vertically down from its equilibrium position and then released. Assume that the pulley is light and smooth, strings and springs are light.

What is Phase of SHM?

A body of mass m is attached to lower end of a spring whose upper end is fixed. The spring has negligible mass. When the mass m is slightly pulled down and released, it oscillates with a time period of 3s. When the mass m is increased by 1 kg, the time period of oscillations becomes 5s. Find the value of m is kg.

A block whose mass is 1 kg is fastened to a spring. The spring has a spring constant of 50 Nm^-1. The block is pulled to a distance x = 10 cm from its equilibrium position at x = 10 on a frictionless surface from rest at t = 0. Calculate the kinetic, potential and total energies of the block when it is 5 cm away from the mean position.

What are transverse waves? Give one example.

A train moves towards a stationary observer with speed 34 m/s. The train' sounds a whistle and its frequency registered by the observer is f_1. the train's speed is reduced to 17 m/s, the frequency registered is f₂. If the speed of sound is 340 m/s, then find the ratio f_1/f_2.