Question

1. Choose the correct option.

i) [L1

M1

T-2] is the dimensional formula for

(A) Velocity (B) Acceleration

(C) Force (D) Work

ii) The error in the measurement of the

sides of a rectangle is 1%. The error in

the measurement of its area is

(A) 1% (B) 1/2%

(C) 2% (D) None of the above.

iii) Light year is a unit of

(A) Time (B) Mass

(C) Distance (D) Luminosity

iv) Dimensions of kinetic energy are the

same as that of

(A) Force (B) Acceleration

(C) Work (D) Pressure

v) Which of the following is not a

fundamental unit?

(A) cm (B) kg

(C) centigrade (D) volt

2. Answer the following questions.

i) Star A is farther than star B. Which star

will have a large parallax angle?

ii) What are the dimensions of the quantity

l l / g , l being the length and g the

acceleration due to gravity?

iii) Define absolute error, mean absolute

error, relative error and percentage error.

iv) Describe what is meant by significant

figures and order of magnitude.

v) If the measured values of two quantities

are A ± ∆A and B ± ∆B, ∆A and ∆B

being the mean absolute errors. What is

the maximum possible error in A ± B?

Show that if Z A

B =





Z

Z

A

A

B

B



vi) Derive the formula for kinetic energy of

a particle having mass m and velocity v

using dimensional analysis

3. Solve numarical examples.

i) The masses of two bodies are measured

to be 15.7 ± 0.2 kg and 27.3 ± 0.3 kg.

What is the total mass of the two and the

error in it?

[Ans : 43 kg, ± 0.5 kg]

ii) The distance travelled by an object in

time (100 ± 1) s is (5.2 ± 0.1) m. What is

the speed and it's relative error?

[Ans : 0.052 ms-1, ± 0.0292 ms-1]

iii) An electron with charge e enters a

uniform. magnetic field B



with a

velocity v



. The velocity is perpendicular

to the magnetic field. The force on the

charge e is given by

| F Bev

|= Obtain the dimensions of B



.

[Ans: [L0

M1

T-2I-1]]

iv) A large ball 2 m in radius is made up of

a rope of square cross section with edge

length 4 mm. Neglecting the air gaps in

the ball, what is the total length of the

rope to the nearest order of magnitude?

[Ans : ≈106 m = 103

km]

v) Nuclear radius R has a dependence on

the mass number (A) as R =1.3×10-

16A1/3 m. For a nucleus of mass number

A=125, obtain the order of magnitude of

R expressed in metre.

[Ans : -15]

vi) In a workshop a worker measures the

length of a steel plate with a Vernier

callipers having a least count 0.01 cm.

Four such measurements of the length

yielded the following values: 3.11 cm,

3.13 cm, 3.14 cm, 3.14 cm. Find the

mean length, the mean absolute error

and the percentage error in the measured

value of the length.

[Ans: 3.13 cm, 0.01 cm, 0.32%]​

Answer 1

Answer:

Q1 1st ka Force hai ... because we know that its dimensional formula is MLT-2....

2ND KA ACC TO ME 2% BECAUSE ERRORS ALWAYS ADDED ...

3RD KA C HAI....CONFIRMED...

4th ka Work hai....

5th a. cm

Q2..

iii. u dont need to learn definations... they will not come in paper..

rest I have not studied yet...

Answer 2

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Question 1 Answers :-

1. d
2. a
3. c
4. d
5. b