Answer to Question #97462 in Mechanics | Relativity for Orogun David

Question

ASSIGNMENT ONE
1. Show that the equation V2 – U2 = 2ax is dimensionally correct.
2. The period T of a simple pendulum is expressed by: √ where ‘l’ is
the length of the pendulum and ‘g’ is the acceleration due to gravity. Show
that the formula is dimensionally consistent.
3. The gravitational force of attraction F between two particles m1 and m2
separated by distance ‘r’ is given as ( ) If ‘K’ is a dimensional constant and its dimension is given as , find the values of x, y and z respectively.
4. A stone is thrown up from a platform with an initial velocity of 19.8 m/s. if the top of the platform is taken to be the ground level, calculate, (a) the time taken to reach the maximum height, (b) the maximum height reach by the stone (c) its velocity just before reaching the ground and (d) total time taken to reach back to the top of the platform.
5. Findthescalarproductof

Answer 1

1.

Dimension of $v^2\ and\ u^2=[L^2T^{-2}]$

Dimension of 2ax $=[LT^{-2}][L]=[L^2T^{-2}]$

So this equation is dimensionally correct

2.

Dimension of T=$[T]$

Dimension of $\sqrt{\frac{l}{g}}=[L^{0.5}][L^{0.5}T^{-1}]^{-1}=[T]$

Hence formula is dimensionally consistent

4.

(a) Time taken to reach max height$=\frac{u}{g}=\frac{19.8}{9.8}=2.02\ sec$

(b). Max height$=\frac{u^2}{2g}=20\ m$

(c) its velocity just before reaching the ground-

$v=-u=-19.8\ m\ s^{-1}$

(d).

Total time = upward time + downward time

$$=2.02+2.02=4.04\ sec$$