Question

If time (t), energy (E) and momentum (P) taken as
base quantities then dimension of mass (m), is
(1) m = ktP2E.
(2) m = ktºP2E
(3) m = ktºP2E-1
(4) m = ktºp-1E2



help ! help ! help !!!!​

Answer 1

Answer:

only option 3 matches the dimension of mass hence option is correct

Answer 2

Answer:

$m=Kt^0{P^2}{E^{-1}}$

Explanation:

Given

t=Time

E=Energy

P=Momentum

m=Mass

We know that kinetic energy of  mass m given as

$E=\dfrac{1}{2}\dfrac{P^2}{m}$

$m=\dfrac{1}{2}\dfrac{P^2}{E}$

Lets take 1/2 is a constant K

$m=K{P^2}{E^{-1}}$

$m=Kt^0{P^2}{E^{-1}}$

There is no any terms of time that is why it have power zero.Because we know that zero power of anything will be 1.

That is why answer is (3)

$m=Kt^0{P^2}{E^{-1}}$