Question

If a particle is moving on an elliptical path given by $\overset{\rightarrow}{r}$ = b coswt $\widehat{i}$ + a sin wt$\widehat{j}$, then find its radial acceleration along $\overset{\rightarrow}{r}$-

• A. w$\overset{\rightarrow}{r}$
• B. w²$\overset{\rightarrow}{r}$
• C. – w²$\overset{\rightarrow}{r}$
• D. None

Answer 1

Answer: (C)

– w²$\overset{\rightarrow}{r}$

Answer 2

$\overset{\rightarrow}{r}$ = b cos wt $\widehat{i}$ + a sin wt $\widehat{j}$

$\frac{d\overset{\rightarrow}{r}}{dt}$ = – bw sin wt$\widehat{i}$ + aw cos wt $\widehat{j}$

$\frac{d^{2}\overset{\rightarrow}{r}}{dt^{2}}$ = – bw² cos wt $\widehat{i}$ – aw² sin wt$\widehat{j}$

= – w² (b cos wt $\widehat{i}$ + a sin wt $\widehat{j}$) = – w²$\overset{\rightarrow}{r}$