A calorie is a unit of heat and equals 4.2 J. Suppose we employ a system of units in which the unit of mass is $α k g,$ the unit of length is $β m e t r e$ and the unit of time is $γ s .$ In this new system, 1 calorie =

see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away

An Intiative by Sri Chaitanya

$4.2 α^{- 1} β^{- 2} γ^{2}$

$4.2 α β^{2} γ^{- 2}$

$α β^{2} γ^{2}$

$α^{- 1} β^{- 2} γ^{2}$

answer is D.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

$[C a l o r i e] = [M L^{2} T^{- 2}]$

Comparing with general dimensional formula $[M^{a} L^{b} T^{c}],$ we get a =1, b = 2, c = 2

$n_{2} = 4.2 {[\frac{1 k g}{α k g}]}^{1} {[\frac{1 m}{β m}]}^{2} {[\frac{1 s}{γ s}]}^{- 2} = 4.2 α^{- 1} β^{- 2} γ^{2}$

Watch 3-min video & get full concept clarity

JEE

NEET

Foundation JEE

Foundation NEET

CBSE