Question

An electric motor of power P is connected with a pulley and a string, to which a mass m is hanging The maximum speed at which mass can be raised
(A)p/2mg
(B)p/mg
(C)p/3mg

(D)3p/mg​

Answer 1

Answer:

(B) p/mg

Explanation:

Given:

• Power = P
• Mass = m

To find:

• Speed (v) = ?

Solution:

We know, Power = Force × velocity.

By, second law of motion we comes to know that, Force = mass × acceleration due to gravity.

$\:$

$\longrightarrow$ P = mg × v

$\:$

$\longrightarrow\:\sf{\dfrac{P}{mg}\:=\:v}$

$\:$

$\longrightarrow\:\sf{\underline{\underline{\therefore\:(B)\:p/mg\:is\:the\:speed\:at\:which\:mass\:can\:be\:raised.}}}$

Answer 2

Given:

Power of the electric motor = P

Mass = m

To find:

The maximum speed at which the mass can be raised.

Solution:

We know that Force (f) = mass (m) * acceleration (a)

Power = work/ time (t)

Where Work = Force* displacement

Force = gravitational force on the mass due to gravity = mg

Therefore, power = mg*S / t = mg* v

Power (P) = mg*v

v = P / mg

Therefore the maximum speed at which the mass can be raised = P/mg (Option B).