Question

The power of a motor is $1600$ watt. If the unit of mass is doubled and units of length and time are halved, the power of the motor in new system is:

• A. 400 units
• B. 6400 units
• C. 3200 units
• D. 4800 units

Answer 1

The correct option is B 6400 units

$P=M^1{L}^2{T}^{-3}$

$\frac{P_1}{P_2}=\frac{M_1^1{L}_1^2{T}_1^{-3}}{M_2^1{L}_2^2{T}_2^{-3}}$

Now,

$M_2=2M_1,L_2=\frac{1}{2}{L}_1,T_2=\frac{1}{2}{T}_1\Rightarrow \frac{P_1}{P_2}=\frac{1}{4}\Rightarrow P_2=4P_1$

$P_2=4\times 1600=6400watt$