Physics 4 Marks Question

3. Pressure.
4. Energy per unit volume.

Explantion:

$\text{[Work done] = [ML}^2\text{ T}^{-2}]$

$\text{[Linear momentum] = [MLT}^{-1}]$

$\text{[Pressure] = [ML}^{-1}\text{T}^{-2}]$

$\text{[Energy per unit volume] = [ML}^{-1}\text{T}^{-2}]$

From the above, we can see that pressure and energy per unit volume have the same dimension, i.e., $\text{ML}^{-1}\text{T}^{-2}.$

4. $\text{n}\propto\frac{1}{\text{u}}$

Explanation:

The larger the unit used to express the physical quantity, the lesser will be the numerical value.

Example: 1kg of sugar can be expressed as 1000g or 10000mg of sugar.

Here, g (gram) is the larger quantity as compared to mg (milligram), but the numerical value used with gram is lesser than the numerical value used with milligram.

1. 0

Explantion:

[ax] = [x²]

⇒ [a] = [x] ...(1)

Dimension of LHS = Dimension of RHS

$\Rightarrow\Big[\frac{\text{dx}}{\sqrt{\text{x}}^2}\Big]=\big[\text{a}^{\text{n}}\big]$

$\Rightarrow\Big[\frac{\text{L}}{\text{L}}\Big]=\big[\text{a}^{\text{n}}\big] \ ...(2)$

$\Rightarrow\big[\text{L}^{0}\big]=[\text{a}^{\text{n}}]$

$\text{n}=0$