Science (English Medium) इयत्ता ११ - CBSE Question Bank Solutions

Consider a pair of identical pendulums, which oscillate with equal amplitude independently such that when one pendulum is at its extreme position making an angle of 2° to the right with the vertical, the other pendulum makes an angle of 1° to the left of the vertical. What is the phase difference between the pendulums?

A cylindrical log of wood of height h and area of cross-section A floats in water. It is pressed and then released. Show that the log would execute S.H.M. with a time period. `T = 2πsqrt(m/(Apg))` where m is mass of the body and ρ is density of the liquid.

A tunnel is dug through the centre of the Earth. Show that a body of mass ‘m’ when dropped from rest from one end of the tunnel will execute simple harmonic motion.

A simple pendulum of time period 1s and length l is hung from a fixed support at O, such that the bob is at a distance H vertically above A on the ground (Figure). The amplitude is θ₀. The string snaps at θ = θ₀/2. Find the time taken by the bob to hit the ground. Also find distance from A where bob hits the ground. Assume θ_o to be small so that sin θ_o = θ_o and cos θ_o = 1.

A tuning fork A, marked 512 Hz, produces 5 beats per second, where sounded with another unmarked tuning fork B. If B is loaded with wax the number of beats is again 5 per second. What is the frequency of the tuning fork B when not loaded?

When two waves of almost equal frequencies n₁ and n₂ reach at a point simultaneously, what is the time interval between successive maxima?

One mole of an ideal gas at standard temperature and pressure occupies 22.4 L (molar volume). What is the ratio of molar volume to the atomic volume of a mole of hydrogen? (Take the size of hydrogen molecule to be about 1Å). Why is this ratio so large?

The Sun is a hot plasma (ionized matter) with its inner core at a temperature exceeding 10⁷ K, and its outer surface at a temperature of about 6000 K. At these high temperatures, no substance remains in a solid or liquid phase. In what range do you expect the mass density of the Sun to be, in the range of densities of solids and liquids or gases? Check if your guess is correct from the following data: mass of the Sun = 2.0 × 10³⁰ kg, radius of the Sun = 7.0 × 10⁸ m.

Estimate the average mass density of a sodium atom assuming its size to be about 2.5 Å. (Use the known values of Avogadro’s number and the atomic mass of sodium). Compare it with the density of sodium in its crystalline phase: 970 kg m^–3. Are the two densities of the same order of magnitude? If so, why?

Does the escape speed of a body from the earth depend on

(a) the mass of the body,

(b) the location from where it is projected,

(c) the direction of projection,

(d) the height of the location from where the body is launched?

The escape speed of a projectile on the earth’s surface is 11.2 km s^–1. A body is projected out with thrice this speed. What is the speed of the body far away from the earth? Ignore the presence of the sun and other planets

Two stars each of one solar mass (= 2× 10³⁰ kg) are approaching each other for a head on collision. When they are a distance 109 km, their speeds are negligible. What is the speed with which they collide? The radius of each star is 104 km. Assume the stars to remain undistorted until they collide. (Use the known value of G).

The potential energy function for a particle executing linear simple harmonic motion is given by V(x) =`(kx^2)/2`, where k is the force constant of the oscillator. For k = 0.5 N m^–1, the graph of V(x) versus x is shown in the figure. Show that a particle of total energy 1 J moving under this potential must ‘turn back’ when it reaches x = ± 2 m.

When a conservative force does positive work on a body, the potential energy of the body ______.

A body of mass 0.5 kg travels in a straight line with velocity v = `ax^(3/2)` where a = `5 m^(1/2)` s^-1. What is the work done by the net force during its displacement from x = 0 to x = 2 m?

One end of a string of length l is connected to a particle of mass m and the other to a small peg on a smooth horizontal table. If the particle moves in a circle with speed the net force on the particle (directed towards the centre) is:

T is the tension in the string.

A body of mass 5 kg is acted upon by two perpendicular forces 8 N and 6 N. Give the magnitude and direction of the acceleration of the body.

A truck starts from rest and accelerates uniformly at 2.0 m s^–2. At t = 10 s, a stone is dropped by a person standing on the top of the truck (6 m high from the ground).

1. What are the velocity, and
2. acceleration of the stone at t = 11?(Neglect air resistance.)

Explain why a horse cannot pull a cart and run in empty space.

A car weighs 1800 kg. The distance between its front and back axles is 1.8 m. Its centre of gravity is 1.05 m behind the front axle. Determine the force exerted by the level ground on each front wheel and each back wheel.