List of practice Questions

Two metallic spheres of radii 1 cm and 3 cm are given charges of -1×10⁻²C and 5×10⁻²C respectively. If these are connected by a conducting wire, the final charge on the bigger sphere is
In a region, the potential is represented by V(x,y,z)=6x-8xy-8y+6yz, where V is in volts and x,y,z are in metres. The electric force experienced by a charge of 2 coulomb situated at point (1,1,1) is:
Which of the following quantities does not change when a resistor connected to a battery is heated due to the current?
One kilogram of ice at 0C is mixed with one kilogram of water at 80C. The final temperature of the mixture is (Take specific heat of water = 4200J kg⁻¹K⁻¹, Latent heat of ice = 336kJ kg⁻¹)
In the equation PV^γ=constant, the value of γ is unity. Then the process is
An ideal refrigerator has a freezer at a temperature of 130C. The coefficient of performance of the engine is 5. The temperature of the air (to which heat is rejected) is
3 moles of an ideal gas at temperature 27C are mixed with 2 moles of an ideal gas at temperature 227C. Determine the equilibrium temperature of the mixture, assuming no loss of energy.
A simple pendulum has time period T. Its time period in a lift which is moving upwards with acceleration 3m s⁻² is
A wave y=a(ω t-kx) on a string meets with another wave producing a node at x=0. Then the equation of the unknown wave is
Suppose the gravitational force varies inversely as the nth power of distance. Then the time period of a planet in circular orbit of radius R around the sun will be proportional to
Two planets A and B have the same material density. If the radius of A is twice that of B, then the ratio of the escape velocity vA/vB is
The upper end of a wire of diameter 12 mm and length 1 m is clamped and its other end is twisted through an angle of 30^. The angle of shear is
Two mercury drops (each of radius r) merge to form a bigger drop. The surface energy of the bigger drop, if the surface tension is T, is
Two circular plates of radius 5 cm each have a 0.01 mm thick water film between them. What will be the force required to separate these plates? (Surface tension of water = 73 dyne/cm)
A spring is compressed between two toy carts of mass m₁ and m₂. When the toys are released, the springs exert equal and opposite average forces for the same time on each cart. If v₁ and v₂ are the velocities of the toy carts and there is no friction between the toy carts and the ground, then:
The potential energy for a force field is given by U(x,y) = (x+y). The force acting on a particle at position given by coordinates (0, π/4) is:
A long string is stretched by 2 cm and the potential energy is V. If the spring is stretched by 10 cm, its potential energy will be
The ratio of the accelerations for a solid sphere (mass m and radius R) rolling down an incline of angle θ without slipping and slipping down the incline without rolling is
A system consists of three particles each of mass m and located at (1,1), (2,2) and (3,3). The coordinates of the centre of mass are
The position x of a particle varies with time t as x = At² - Bt³. The acceleration at the time of the maximum velocity will be equal to zero. What is the value of t?
Two projectiles A and B are thrown with the same speed but at angles 40^ and 50^ with the horizontal. Then
A body is travelling in a circle at a constant speed. It
If P represents radiation pressure, c represents speed of light and Q represents radiation energy striking a unit area per second, the non-zero integers x, y and z such that Pˣ Qʸ cᶻ is dimensionless, are:
She always praises everything I say.
He refused to be led by the nose.