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

Answer the following question.

Define the binding energy of a satellite.

On the basis of dimensions, decide which of the following relations for the displacement of a particle undergoing simple harmonic motion is not correct ______.

1. y = `a sin  (2πt)/T`
2. y = `a sin vt`
3. y = `a/T sin (t/a)`
4. y = `asqrt(2) (sin  (2pit)/T - cos  (2pit)/T)`

If P, Q, R are physical quantities, having different dimensions, which of the following combinations can never be a meaningful quantity?

1. (P – Q)/R
2. PQ – R
3. PQ/R
4. (PR – Q²)/R
5. (R + Q)/P

A function f(θ) is defined as: `f(θ) = 1 - θ + θ^2/(2!) - θ^3/(3!) + θ^4/(4!)` Why is it necessary for q to be a dimensionless quantity?

Why length, mass and time are chosen as base quantities in mechanics?

Give an example of a physical quantity which has a unit but no dimensions.

Give an example of a physical quantity which has neither unit nor dimensions.

The volume of a liquid flowing out per second of a pipe of length l and radius r is written by a student as `v = π/8 (pr^4)/(ηl)` where P is the pressure difference between the two ends of the pipe and η is coefficient of viscosity of the liquid having dimensional formula ML^–1 T^–1. Check whether the equation is dimensionally correct.

In the expression P = E l² m^–5 G^–2, E, m, l and G denote energy, mass, angular momentum and gravitational constant, respectively. Show that P is a dimensionless quantity.

If velocity of light c, Planck’s constant h and gravitational contant G are taken as fundamental quantities then express mass, length and time in terms of dimensions of these quantities.

An artificial satellite is revolving around a planet of mass M and radius R, in a circular orbit of radius r. From Kepler’s Third law about the period of a satellite around a common central body, square of the period of revolution T is proportional to the cube of the radius of the orbit r. Show using dimensional analysis, that `T = k/R sqrt(r^3/g)`. where k is a dimensionless constant and g is acceleration due to gravity.

Einstein’s mass-energy relation emerging out of his famous theory of relativity relates mass (m ) to energy (E ) as E = mc², where c is speed of light in vacuum. At the nuclear level, the magnitudes of energy are very small. The energy at nuclear level is usually measured in MeV, where 1 MeV= 1.6 × 10^–13 J; the masses are measured in unified atomic mass unit (u) where 1u = 1.67 × 10^–27 kg.

1. Show that the energy equivalent of 1 u is 931.5 MeV.
2. A student writes the relation as 1 u = 931.5 MeV. The teacher points out that the relation is dimensionally incorrect. Write the correct relation.

A uniformly moving cricket ball is turned back by hitting it with a bat for a very short time interval. Show the variation of its acceleration with time. (Take acceleration in the backward direction as positive).

For a particle performing uniform circular motion, choose the correct statement(s) from the following:

1. Magnitude of particle velocity (speed) remains constant.
2. Particle velocity remains directed perpendicular to radius vector.
3. Direction of acceleration keeps changing as particle moves.
4. Angular momentum is constant in magnitude but direction keeps changing.

A cyclist starts from centre O of a circular park of radius 1 km and moves along the path OPRQO as shown figure. If he maintains constant speed of 10 ms^–1, what is his acceleration at point R in magnitude and direction?

Earth can be thought of as a sphere of radius 6400 km. Any object (or a person) is performing circular motion around the axis of earth due to earth’s rotation (period 1 day). What is acceleration of object on the surface of the earth (at equator) towards its centre? what is it at latitude θ? How does these accelerations compare with g = 9.8 m/s²?

Earth also moves in circular orbit around sun once every year with on orbital radius of 1.5 × 10¹¹ m. What is the acceleration of earth (or any object on the surface of the earth) towards the centre of the sun? How does this acceleration compare with g = 9.8 m/s²?

A person driving a car suddenly applies the brakes on seeing a child on the road ahead. If he is not wearing seat belt, he falls forward and hits his head against the steering wheel. Why?

When a body slides down from rest along a smooth inclined plane making an angle of 45° with the horizontal, it takes time T. When the same body slides down from rest along a rough inclined plane making the same angle and through the same distance, it is seen to take time pT, where p is some number greater than 1. Calculate the co-efficient of friction between the body and the rough plane.

A racing car travels on a track (without banking) ABCDEFA (Figure). ABC is a circular arc of radius 2 R. CD and FA are straight paths of length R and DEF is a circular arc of radius R = 100 m. The co-efficient of friction on the road is µ = 0.1. The maximum speed of the car is 50 ms^–1. Find the minimum time for completing one round.