Question

The correct order in which the dimensions of time decreases in the following physical quantities is
1. Stefan's constant
2. Coefficient of volume expansion
3. Work done
4. Velocity gradient

• A. 2,4,3,1
• B. 1,2,3,4
• C. 4,3,2,1
• D. 1,2,4,3

Answer 1

Answer: (A)

1. Stefan's coefficient
$=\frac{\text { Energy }}{\text { Time } \times \text { Area } \times \text { (Temperature) }^{4}}$
$=\frac{\left[ ML ^{2} T ^{-2}\right]}{[ T ]\left[ L ^{2}\right][ K ]^{4}}$
$=\left[ ML ^{0} T ^{-3} K ^{-4}\right]$
2. Coefficient of volume expansion,
$=\frac{\text { Change in volume }}{\text { Original volume } \times \text { Temperature }}$
$=\frac{\left[ L ^{3}\right]}{\left[ L ^{3}\right][ K ]}$
$=\left[ M ^{0} L ^{0} T ^{0} K ^{-1}\right]$
3. Work done $=$ Force $\times$ Distance
$=\left[ MLT ^{-2}\right][ L ]=\left[ ML ^{2} T ^{-2}\right]$
4. Velocity gradient $=\frac{\text { Velocity }}{\text { Distance }}$
$=\frac{\left[ LT ^{-1}\right]}{[ L ]}=\left[ T ^{-1}\right]=\left[ M ^{0} L ^{0} T ^{-1}\right]$
The correct order is (a) : 2,4,3,1