Question

dimensional formula of acceleration due to gravity

Answer 1

M^0L^1T^-2
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Dimensional formula of acceleration due to gravity is M^0L^1T^-2.

The dimensional formula of acceleration due to gravity is same as acceleration.

The acceleration due to gravity is denoted by 'g' and g = 9.8 m/s².

Answer 2

Answer:

$g=\left[M^{0} L^{1} T^{-2}\right]$

Explanation:

Dimensional Formula of Acceleration Due To Gravity

The dimensional formula of Acceleration Due To Gravity is given by,

$\left[\mathrm{M}^{0} \mathrm{~L}^{1} \mathrm{~T}^{-2}\right]$

Where,

$\mathrm{M}= Mass$

L = Length

T = Time

Derivation

Since, $Force = Mass \times Acceleration$

$\therefore Acceleration (g)= Force \times\left[\right. Mass ^{-1} \ldots$ . .(1)

$\Rightarrow$ Dimensional formula of the mass $=\left[\mathrm{M}^{1} \mathrm{~L}^{0} \mathrm{~T}^{0}\right] \ldots (2)$

Also, the dimensions of Force $=\left[M^{1} L^{1} T^{-2}\right] \ldots (3)$

On substituting equation (2) and (3) in equation (1) we get,

Acceleration due to gravity$= Force \times [Mass ^{-1}$

Or, $g=\left[M^{1} L^{1} T^{-2}\right] \times\left[M^{1} L^{0} T^{0}\right]^{-1}=\left[M^{0} L^{1} T^{-2}\right]$.

Therefore, acceleration due to gravity is dimensionally represented as $g=\left[M^{0} L^{1} T^{-2}\right]$

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