Class 11th

In a simple harmonic oscillation, what fraction of total mechanical energy is in the form of kinetic energy, when the particle is midway between mean and extreme position.

A monoatomic ideal gas, initially at temperature T?, is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature T? by releasing the piston suddenly. If ? and ? are the lengths of the gas column, before and after the expansion respectively, then the value of T?/T? will be :

The force is given in terms of time t and displacement x by the equation
F = A cos Bx + C sin Dt
The dimensional formula of AD/B is :

The instantaneous velocity of a particle moving in a straight line is given as v = αt + βt², where α and β are constants. The distance travelled by the particle between 1s and 2s is :

A heat engine has an efficiency of 1/6. When the temperature of sink is reduced by 62°C, its efficiency get doubled. The temperature of the source is :

Two spherical soap bubbles of radii r₁ and r₂ in vacuum combine under isothermal conditions. The resulting bubble has radius equal to :

Two different metal bodies A and B of equal mass are heated at a uniform rate under similar conditions. The variation of temperature of the bodies is graphically represented as shown in the figure. The ratio of specific heat capacities is :
(The graph shows Temperature (°C) on the y-axis and Time (s) on the x-axis. Both A and B are straight lines starting from the origin. For body A, temperature reaches 120°C in 4s. For body B, temperature reaches 90°C in 6s.)

A force F = (40î + 10?)N acts on a body of mass 5 kg. If the body starts from rest, its position vector r at time t = 10s, will be :

Consider a planet in some solar system which has a mass double the mass of earth and density equal to the average density of earth. If the weight of an object on earth is W, the weight of the same object on that planet will be :

Two billiard balls of equal mass 30g strike a rigid wall with same speed of 108 kmph (as shown) but at different angles. If the balls get reflected with the same speed then the ratio of the magnitude of impulses imparted to ball 'a' and ball 'b' by the wall along 'X' direction is :
(Diagram shows ball 'a' hitting the wall perpendicularly along the x-axis and ball 'b' hitting the wall at a 45° angle to the x-axis.)