A body of moment of inertia 6 kg m² rotating with an angular velocity 2 rad/s has the same kinetic energy as a mass of 6 kg moving with a velocity of?

A sphere of radius 1 m and mass 1 kg along a horizontal plane with constant speed 1 m/s. It encounters an inclined plane at angle 50 degrees and climbs upward. Assuming that it rolls without slipping how far up the sphere will travel?

(I_CM = 2/5 MR²)

The angular velocity of a rotating disk with a radius of 2 m decreases from 6 rad/s to 3 rad/s in 2 seconds. What is the linear acceleration of a point on the edge of the disk during this time interval?

A 515 kg roller coaster is at the bottom of a loop with a radius of 9.8 m. If the acceleration at the bottom of the loop is 20 m/s², Find the force exerted on the roller coaster by the loop at the bottom.

A 1 kg object, attached to a 0.5 m string, rotates in a horizontal circle with the string at an angle 30 degrees to the vertical line. Calculate the tension on the string.

A 1 kg object, attached to a 0.5 m string, does 4 horizontal circular motion in one second. Calculate the tension on the string.  

A 1.75 kg of object moves in SHM as follows: x = 4cos(1.33t-3π/2), where x in metre and t in second. Find total mechanical energy.

 The graph shows displacement versus time for a particle of a uniform medium as a wave passes to the left direction through the medium. If the wavelength of the wave is 0.2π m, Find the vibrational velocity of the particle when t = 0.01 s and x = 0.005 m.

A block is attached to a ceiling by a spring of force constant, k. When pulled down and released, the block undergoes SHM. The motion of the block is shown in the graph, where x in centimetre and t in second. From the graph, where is the position of the block at 4 seconds?

A circular metal column is to support a load of 500 kg and it must not compress more than 0.1 mm. The modulus of elasticity (Young modulus) is 210x10⁹ N/m². If the initial length of the column is 2 m long, calculate the cross-sectional area of the column.

Calculate the energy stored in a 2 m long copper wire of a cross-sectional area of 0.5 mm² if a force of 50 N is applied to it. (Y_copper =1.2×10¹¹ Pa)

The force per cross sectional area is 1.5x10⁶ N/m² and the elongation per unit length is 3 x 10^-2.    

Find the young modulus of the wire.

Based on the graph, find the total work done during the deformation.

Consider air inside a pump as a thermodynamic system having initial volume V at atmospheric pressure and room temperature, 27°C. Then the pump decreases to a volume 1/4 of V. Calculate the final temperature of air in the pump? (adiabatic compression).

The graph shows one mole of monoatomic gas expanding isobarically at a constant pressure of 2.5 × 10⁵ Pa. It is then cooled down at constant volume to a pressure of 1.2 × 10⁵ Pa. The gas is finally compressed isothermally back to its initial state. Calculate the heat change during the process AB when the change in internal energy during AB is 5852 J (temperature increased during AB).

A beaker with an internal volume of 0.083 cubic meters has a sample of an ideal gas which has a pressure of 210 kPa at room temperature 20-degree Celsius. Determine the number of moles of gas in the beaker.

Calculate the temperature at which 0.654 moles of neon gas occupies 12.30 litres at 1.95 atmospheres.

Two moles of oxygen gas expand isothermally at 290 K. Its volume changes from 20 liters to 30 liters. Calculate the work done by the gas.

A compressor expands the air in a cylinder at a constant pressure of 8.6×10⁵ Pa. During the process, the volume of the cylinder increases by 4.05×10^–4 m³ and 9.5 J of energy is transferred out of the cylinder as heat. Calculate the change in the air internal energy.