Question

T=2π×l/g check the correctness

Answer 1

We are given to check the correctness of the equation,

$\displaystyle\longrightarrow\sf{T=2\pi\cdot\dfrac {l}{g}}$

where,

• $\displaystyle\sf {T=}$ time period (of a simple pendulum)

• $\displaystyle\sf {l=}$ length (of string)

• $\displaystyle\sf {g=}$ acceleration due to gravity

The dimension of time period is,

• $\displaystyle\sf {[T]=T\quad\quad\dots (1)}$

The dimension of length is,

• $\displaystyle\sf {[L]=L}$

The dimension of acceleration due to gravity is,

• $\displaystyle\sf {[g]=L\,T^{-2}}$

The term $\displaystyle\sf {2\pi}$ is a dimensionless constant.

Hence,

$\displaystyle\longrightarrow\sf{\left[\dfrac {l}{g}\right]=\dfrac {L}{L\,T^{-2}}}$

$\displaystyle\longrightarrow\sf{\left[\dfrac {l}{g}\right]=\dfrac {1}{T^{-2}}}$

$\displaystyle\longrightarrow\sf{\left[\dfrac {l}{g}\right]=T^2\quad\quad\dots (2)}$

From (1) and (2),

$\displaystyle\longrightarrow\sf {\underline {\underline {[T]\neq\left [\dfrac {l}{g}\right]}}}$

Thus the equation is not correct.

Answer 2

Answer:

Explanation: ur answer