Question

The questions which follow consist of two statements labelled 'A' and 'R'. Examine each statement
carefully, and decide, if assertion 'A' and reason 'R' are individually correct. If so then decide, whether, the
reason 'R' is the correct explanation of A. Select your answer, using the codes given below, and write your answer

(A) In terms of mass, length, and time, the unit of work is kgm²s^-2.
(R) Work is the product of force and displacement. The unit of force is kg ms^-2 and displacement is 'm'. So, the unit of work is kg m²s^-2.

• A. Both 'A' and 'R' are correct and 'R' is the correct explanation of 'A'
• B. Both 'A' and 'R' are correct, but 'R' is not the correct explanation of 'A'
• C. 'A' is correct, but 'R' is incorrect
• D. 'A' is incorrect, but 'R' is correct

Answer 1

The correct option is A

Both 'A' and 'R' are correct and 'R' is the correct explanation of 'A'

Explanation for Assertion statement

1. Since, work done is defined as the product of the magnitude of the force and displacement travelled by the object in the direction of the applied force.
2. Mathematically, we can say that,

$\mathrm{Work}\mathrm{done}=\mathrm{Force}\mathrm{x}\mathrm{displacement}$

$\mathrm{W}=\mathrm{F}\mathrm{x}\mathrm{s}$

$1\mathrm{J}=1\mathrm{N}\mathrm{x}1\mathrm{m}$

$1\mathrm{J}=1\frac{\mathrm{kg}\mathrm{m}}{{\mathrm{s}}^2}\mathrm{x}1\mathrm{m}$

$1\mathrm{J}=1\frac{\mathrm{kg}{\mathrm{m}}^2}{{\mathrm{s}}^2}$

The dimensions of mass (kg), length (m), and time (t) all are present in the expression.

Explanation for Reason statement

1. The unit of force is kg ms^-2.
2. The unit of displacement is m.
3. Work done is the product of force and displacement will have units as kg m²s^-2.

Therefore, both assertion and reason are individually correct, and the reason is the correct explanation of the assertion statement.

Hence, option (A) is correct.