Question

Which of the following quantities are always positive in a simple harmonic motion?

• A. $\overset{ \rightarrow }{F}.\overset{ \rightarrow }{a}$
• B. $\overset{ \rightarrow }{v}.\overset{ \rightarrow }{r}$
• C. $\overset{ \rightarrow }{a}.\overset{ \rightarrow }{r}$
• D. $\overset{ \rightarrow }{F}.\overset{ \rightarrow }{r}$

Answer 1

Answer: (A)

For a simple harmonic motion, $F=-kx,a=-\left(\omega \right)^{2}xandv=\pm\sqrt{\left(A^{2} - x^{2}\right)}$
Now,
$\overset{ \rightarrow }{F}.\overset{ \rightarrow }{a}=\left(F\right)\left(a\right)cos\theta \because \left(\theta = 0 ^\circ \right)\overset{ \rightarrow }{F}.\overset{ \rightarrow }{a}=k\left(\omega \right)^{2}x^{2}$
Hence, $\overset{ \rightarrow }{F}.\overset{ \rightarrow }{a}$ has a positive value.