Question

if the formula t=2π√Ax/F is dimensionally correct where t is time period, x us distance,F is force then A has dimensions of mass? Explain

Answer 1

Answer:

The dimension of force is MLT^-2. Thus, the dimension of the right-hand side is

$\sqrt{ \frac{m}{ \frac{ml {t}^{ - 2} }{l} } }$

Where, m = Mass, l = Length and t = time.

$\sqrt{ \frac{1}{ {t}^{ - 2} } } = \: t$

The left-hand side is time period and hence the dimension is T. The dimension of both sides are equal and hence the formula is correct.

Answer 2

Answer:

The dimensional formula is correct

Explanation:

Dimension of time period t = M⁰L⁰T¹

= T

Dimension of the distance x = M⁰L¹T⁰

= L

Dimension of the force F = M¹L¹T-²

Dimension of the mass A = M¹L⁰T⁰

= M

LHS = [T]

RHS = √ [M][L]

[MLT-²]

= √ [1/T-²]

= √T²

= [T]

Hence proved