This page focuses on the detailed Unit & measurment question answers for Class 11 Physics Unit & measurment, addressing the question: 'A physical quantity P is related to four observables a, b, c and d as follows :
The percentage errors of measurement in a, b, c and d are 1%, 3%, 4% and 2%, respectively. What is the percentage error in the quantity P ? If the value of P calculated using the above relation turns out to be 3.763, to what value should you round off the result ?'. The solution provides a thorough breakdown of the question, highlighting key concepts and approaches to arrive at the correct answer. This easy-to-understand explanation will help students develop better problem-solving skills, reinforcing their understanding of the chapter and aiding in exam preparation.

Question 13

A physical quantity P is related to four observables a, b, c and d as follows :

The percentage errors of measurement in a, b, c and d are 1%, 3%, 4% and 2%, respectively. What is the percentage error in the quantity P ? If the value of P calculated using the above relation turns out to be 3.763, to what value should you round off the result ?

Answer

= 3x1 +2x3 + ½ x 4 + 2

= 3 + 6 +2 + 2

= 13 %

Percentage error in *P* = 13 %

Value of *P* is given as 3.763.

By rounding off the given value to the first decimal place, we get *P* = 3.8.

- Q:-
State the number of significant figures in the following:

(a) 0.007 m

^{2}(b) 2.64 x 10

^{24}kg(c) 0.2370 g cm

^{-3}(d) 6.320 J

(e) 6.032 N m

^{-2}(f) 0.0006032 m

^{2} - Q:-
Fill in the blanks by suitable conversion of units:

(a) 1 kg m

^{2}s^{–2}= ....g cm^{2 }s^{–2 }(b) 1 m =..... ly

(c) 3.0 m s

^{–2}=.... km h^{–2}(d) G = 6.67 × 10

^{–11}N m^{2}(kg)^{–2}=.... (cm)3s^{–2}g^{–1}. - Q:-
Rain is falling vertically with a speed of 30 m s

^{–1}. A woman rides a bicycle with a speed of 10 m s^{–1}in the north to south direction. What is the direction in which she should hold her umbrella? - Q:- Give the magnitude and direction of the net force acting on

(a) a drop of rain falling down with a constant speed

(b) a cork of mass 10 g floating on water

(c) a kite skillfully held stationary in the sky

(d) a car moving with a constant velocity of 30 km/h on a rough road

(e) a high-speed electron in space far from all material objects, and free of electric and magnetic fields. - Q:-
The mass of a box measured by a grocer's balance is 2.300 kg. Two gold pieces of masses 20.15 g and 20.17 g are added to the box. What is

(a) the total mass of the box,

(b) the difference in the masses of the pieces to correct significant figures?

- Q:-
On an open ground, a motorist follows a track that turns to his left by an angle of 60° after every 500 m. Starting from a given turn, specify the displacement of the motorist at the third, sixth and eighth turn. Compare the magnitude of the displacement with the total path length covered by the motorist in each case.

- Q:-
What amount of heat must be supplied to 2.0 x 10

^{-2}kg of nitrogen (at room temperature) to raise its temperature by 45 °C at constant pressure? (Molecular mass of N^{2}= 28; R = 8.3 J mol^{-1}K^{-1}.) - Q:- In which of the following examples of motion, can the body be considered approximately a point object:

(a) a railway carriage moving without jerks between two stations.

(b) a monkey sitting on top of a man cycling smoothly on a circular track.

(c) a spinning cricket ball that turns sharply on hitting the ground.

(d) a tumbling beaker that has slipped off the edge of a table. - Q:-
A transverse harmonic wave on a string is described by

y(x,t) = 3.0 sin [36t + 0.018x + π /4]

Where x and y are in cm and t in s. The positive direction of x is from left to right.

(a) Is this a travelling wave or a stationary wave? If it is travelling, what are the speed and direction of its propagation?

(b) What are its amplitude and frequency?

(c) What is the initial phase at the origin?

(d) What is the least distance between two successive crests in the wave?

- Q:- Read each statement below carefully and state with reasons, if it is true or false:

(a) The magnitude of a vector is always a scalar

(b) each component of a vector is always a scalar

(c) the total path length is always equal to the magnitude of the displacement vector of a particle

(d) the average speed of a particle (defined as total path length divided by the time taken to cover the path) is either greater or equal to the magnitude of average velocity of the particle over the same interval of time

(e) Three vectors not lying in a plane can never add up to give a null vector.

- Q:-
Read each statement below carefully and state, with reasons, if it is true or false:

(a) The net acceleration of a particle in circular motion is always along the radius of the circle towards the centre

(b) The velocity vector of a particle at a point is always along the tangent to the path of the particle at that point

(c) The acceleration vector of a particle in uniform circular motion averaged over one cycle is a null vector

- Q:-
For any arbitrary motion in space, which of the following relations are true :

(a) v

_{average}= (1/2) (v (t_{1}) + v (t_{2}))(b) v

_{average}= [r(t_{2}) - r(t_{1}) ] / (t_{2}– t_{1})(c) v

_{(t) }= v (0) + a t(d) r

_{(t)}= r (0) + v (0) t + (1/2) a t^{2}(e) a

_{average}=[ v (t_{2}) - v (t_{1})] /( t_{2}– t_{1})(The ‘average’ stands for average of the quantity over the time interval t

_{1}to t_{2}) - Q:-
A drunkard walking in a narrow lane takes 5 steps forward and 3 steps backward, followed again by 5 steps forward and 3 steps backward, and so on. Each step is 1 m long and requires 1 s. Plot the x-t graph of his motion. Determine graphically and otherwise how long the drunkard takes to fall in a pit 13 m away from the start.

- Q:- Pick out the two scalar quantities in the following list: force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, relative velocity.
- Q:-
A train runs along an unbanked circular track of radius 30 m at a speed of 54 km/h. The mass of the train is 10

^{6}kg. What provides the centripetal force required for this purpose - The engine or the rails? What is the angle of banking required to prevent wearing out of the rail? - Q:-
Explain clearly, with examples, the distinction between:

a) magnitude of displacement (sometimes called distance) over an interval of time, and the total length of path covered by a particle over the same interval;

b) magnitude of average velocity over an interval of time, and the average speed over the same interval. [Average speed of a particle over an interval of time is defined as the total path length divided by the time interval]. Show in both (a) and (b) that the second quantity is either greater than or equal to the first.

When is the equality sign true? [For simplicity, consider one-dimensional motion only].

- Q:-
Answer carefully, with reasons:

(a) In an elastic collision of two billiard balls, is the total kinetic energy conserved during the short time of collision of the balls (i.e. when they are in contact)?

(b) Is the total linear momentum conserved during the short time of an elastic collision of two balls?

(c) What are the answers to (a) and (b) for an inelastic collision?

(d) If the potential energy of two billiard balls depends only on the separation distance between their centres, is the collision elastic or inelastic? (Note, we are talking here of potential energy corresponding to the force during collision, not gravitational potential energy).

- Q:-
Given below are some functions of x and t to represent the displacement (transverse or longitudinal) of an elastic wave. State which of these represent (i) a traveling wave, (ii) a stationary wave or (iii) none at all:

(a) y = 2 cos (3x) sin (10t)

(b) y = 2 underroot(x -vt)

(c) y = 3 sin (5x - 0.5t) + 4 cos (5x - 0.5t)

(d) y = cos x sin t + cos 2x sin 2t

- Q:-
Ten one-rupee coins are put on top of each other on a table. Each coin has a mass m. Give the magnitude and direction of

(a) the force on the 7

^{th}coin (counted from the bottom) due to all the coins on its top,(b) the force on the 7

^{th}coin by the eighth coin,(c) the reaction of the 6

^{th }coin on the 7^{th}coin. - Q:-
Which of the following functions of time represent (a) simple harmonic, (b) periodic but not simple harmonic, and (c) non-periodic motion? Give period for each case of periodic motion (ω is any positive constant):

(a) sin ωt - cos wt

(b) sin

^{3}ωt(c) 3 cos (π/4 - 2ωt)

(d) cos ωt + cos 3ωt + cos 5ωt

(e) exp (-ω

^{2}t^{2})

Ipsita
2019-05-28 22:26:54

How do we know to which place should we round it up to?

- NCERT Chapter