Question

A body is moving with uniform speed v on a horizontal circle from A as shown in the fig. Change in velocity in the first quarter revolution is

• A. v²
• B. √2 v southwest
• C. √2 north west
• D. 2v west

Answer 1

Answer: (B)

√2 v southwest

Answer 2

For quarter revolution

$\Delta\overrightarrow{v} = v_{2}\left( - \widehat{i} \right) - v_{1}\widehat{j}$

or $\Delta\overrightarrow{v} = - v\widehat{i} - v\widehat{j}$

∴ ∆v = $\sqrt{v^{2} + v^{2}}$ = $\sqrt{2}v$

Also α = tan^-1$\frac{v}{v} = 45^{o}$

∴ $\Delta\overrightarrow{v} = \sqrt{2}v$ south west.