Question

the unit of power is 10 ∧6 erg/minute ,unit of force is 1000 dyne, and the unit of timeis 10∧-1s. then the unit of mass in the system would be...? options: 2g.....3g.....6g......9g.....

Answer 1

Explanation:

$p = \frac{w}{t}$

w=fx(f--->force ,x ---->displacement)

So,

$10 }^{6} = \frac{1000x}{ {10}^{ - 1} }$

=>x=100 cm

$v = \frac{100}{10 {}^{ - 1} }$

Answer 2

The unit of mass is 6g

Therefore, option (c) is correct.

Explanation:

Given:

unit of power = $10^6$ erg/min = [/tex]\frac{10^6}{60}[/tex] erg/s

Unit of force = $1000$ dyne

Unit of time $=10^{-1}$ s

To find out:

Unit of mass

Solution:

The given units are in CGS system

In this system

1 erg = 1 gm-cm²/s²

1 dyne = 1 gm-cm/s²

We know that

Power = Force × Velocity

Power = Force × (Displacement/Time)

or, Displacement = (Power × Time)/Force

$\implies x=\frac{10^6/60\times 10^{-1}}{1000}$

$\implies x=\frac{10^4}{6\times 1000}$

$\implies x=\frac{5}{3}$ cm

Now

Force = mass × Acceleration

or, Force = Mass × (Velocity/Time)

or, Force =  Mass × (Displacement/Time²)

or, Mass = (Force × Time²)/Displacement

$\implies M=\frac{1000\times (10^{-1})^2}{5/3}$

$\implies M=\frac{10\times 3}{5}$ gram

$\implies M=6$ gram

Hope this answer is helpful.

Know More:

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