If the unit of length, mass and time each is doubled, the unit of work is increased by:

Question

If the unit of length, mass and time each is doubled, the unit of work is increased by: (A) 2 times (B) 6 times (C) 4 times (D) 8 times

Tardigrade Admin · Accepted Answer

The dimensional formula for work done is as W=[ML2T-2] Now, units M, L and T are doubled, then work done becomes W[2M][2L]2[2T]2 W=(2× 4/4)× [ML2T-2] W=2× W Hence, unit of work increases by 2 times.

Q. If the unit of length, mass and time each is doubled, the unit of work is increased by:

2 times

6 times

4 times

8 times

The dimensional formula for work done is as $W = [M L^{2} T^{- 2}]$ Now, units M, L and T are doubled, then work done becomes $W [2 M] [2 L]^{2} [2 T]^{2}$ $W = \frac{2 \times 4}{4} \times [M L^{2} T^{- 2}]$ $W = 2 \times W$ Hence, unit of work increases by 2 times.

Q. If the unit of length, mass and time each is doubled, the unit of work is increased by:

2 times

6 times

4 times

8 times

The dimensional formula for work done is as W=[ML2T−2] Now, units M, L and T are doubled, then work done becomes W[2M][2L]2[2T]2 W=42×4​×[ML2T−2] W=2×W Hence, unit of work increases by 2 times.

The dimensional formula for work done is as $W = [M L^{2} T^{- 2}]$ Now, units M, L and T are doubled, then work done becomes $W [2 M] [2 L]^{2} [2 T]^{2}$ $W = \frac{2 \times 4}{4} \times [M L^{2} T^{- 2}]$ $W = 2 \times W$ Hence, unit of work increases by 2 times.