Question

check the correctness of following formula with help of dimensions . s=u+1/2at^2​

Answer 1

ANSWER:

• The given formula is not correct according to dimensional formula.

GIVEN:

• S = u + 1/2 at².

TO FIND:

• The correctness of the given formula with the help if dimensions.

EXPLANATION:

S = u + 1/2 at².

$\sf The\ unit \ of \ distance\ is \ m\\ \\ \\ \sf [ S ] = [ M^0\ L^1\ T^0 ] \\ \\ \\ \sf The\ unit\ of \ velocity \ is\ ms^{-1}\\ \\ \\ \sf [ u ] = [ M^0\ L^1\ T^{-1} ]\\ \\ \\ \sf \dfrac{1}{2} \ is \ a \ constant\ and\ have\ no\ dimension \\ \\ \\ \sf The\ unit\ of \ velocity \ is\ ms^{-2} \\ \\ \\ \sf The\ unit\ of \ time \ is\ seconds\\ \\ \\ \sf [ at^2] = [M^0 \ L ^{1} \ T^{-2}] \times [M^0 \ L^0 \ T^2] \\ \\ \\ \sf [ at^2] = [M^0 \ L ^{1} \ T^{0}]$

$\sf [ S ] = [ u ] + \left[ \dfrac{1}{2} at^2 \right] \\ \\ \\ \sf [ L ] = [ L \ T^{-1} ] + [ L]\\ \\ \\ \sf Here\ [ L ] \not= [ L \ T^{-1} ],\ \ [ L ] = [ L ]$

Since the dimension of velocity(u) is not matching with the dimension of distance(S), the equation is dimensionally wrong.

Hence the given formula is dimensionally wrong.

EXTRA POINTS:

• If a formula is dimensionally correct, it may or not may not be a valid formula.

• But if a formula is not dimensionally correct, it cannot be a valid formula.

• The quantities with different dimensions cannot be added or subtracted.

• Multiplication and division are possible independent of their dimensions.