Question

If the units of length, velocity and force are halved, then the unit of power will be
doubled
halved
one-fourth
remain unaffected​

Answer 1

Answer:

Explanation:

solution :

Since units of length, velocity and force are doubled.

Hence, [m]=[force][time][velocity],

[time]=[length][velocity]

Hence, unit of mass, and time remains same.

Momentum is  doubled

Answer 2

Answer:

The unit of power will be one-fourth.

Explanation:

• The dimensional formula of velocity = $[LT^{-1} ]$ . If the units of length are halved then velocity gets halved automatically, while the time remains constant.

• Force's dimensional formula $= [MLT^{-1}]$. Mass and time remains constant. But as length decreases to half, force will be halved as well.
• Power's dimensional formula  $=[ML^{2}T^{-3} ]$. As length reduced to half, power's dimensional formula becomes :$[M(\frac{L}{2} )^{2}T^{-2}]= \frac{1}{4} [ML^{2}T^{-2}]$.  

Therefore, the unit of power falls to one-fourth.