1

IIT-JEE 2003

Subjective
If nth divisions of the main scale coincide with (n+1)th divisions of vernier scale. Given one main scale division is equal to 'a' units. Find the least count of the vernier.

Answer

$${a \over {n + 1}}units$$

Explanation

We know that (n + 1) divisions on the vernier scale = n division on the main scale

Therefore,

1 division on the vernier scale = $$\left( {{n \over {n + 1}}} \right)$$ divisions on the main scale = $$\left( {{n \over {n + 1}}} \right)a$$ units

Therefore, the least count (LC) of the vernier caliper is

$$1(MSD) - 1(VSD) = a - \left( {{n \over {n + 1}}} \right)a = {a \over {n + 1}}$$
2

IIT-JEE 1990

Subjective

Column - I gives the three physical quantities. Select the appropriate units for the choices given in Column - II. Some of the physical quantities may have more than one choice correct:

Column I Column II
Capacitance (i) ohm-second
Inductance (ii) coulomb2 - joule-1
Magnetic Induction (iii) coulomb (volt)-1
(iv) newton (amp-meter)-1
(v) volt-second (ampere)-1

Answer

Capacitance - coulomb (volt)-1, coulomb2 - joule-1

Inductance - ohm-second, volt-second (ampere)-1

Magnetic Induction - newton (amp-meter)-1

3

IIT-JEE 1983

Subjective
Match the physical quantities given in column I with dimension expressed in terms of mass (M), length (L), time (T), and charge (Q) given in column II and write the correct answer against the matched quantity in a tabular form in your answer book.
Column I Column II
Angular Momentum ML2T-2
Latent heat ML2Q-2
Torque ML2T-1
Capacitance ML3T-1Q-2
Inductance M-1L-2T2Q2
Resistivity L2T-2

Answer

Angular Momentum - ML2T-1

Latent heat - L2T-2

Torque - ML2T-2

Capacitance - M-1L-2T2Q2

Inductance - ML2Q-2

Resistivity - ML3T-1Q-2

4

IIT-JEE 1982

Subjective
Write the dimensions of the followings in terms of mass, time, length and charge
(i) magnetic flux
(ii) rigidity modulus

Answer

(i) [ M1L2T-1Q-1 ]
(ii) [ ML-1T-2 ]

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