Question

Initially the spring is undeformed. Now the force ${}^{\prime }{F}^{\prime }$ is applied to ${}^{\prime }{B}^{\prime }$ as shown in the figure. When the displacement of ${}^{\prime }{B}^{\prime }$ w.r.t. ${}^{\prime }{A}^{\prime }$ is ${}^{\prime }{x}^{\prime }$ towards right in some time, then the relative acceleration of ${}^{\prime }{B}^{\prime }$ w.r.t ${}^{\prime }{A}^{\prime }$ at that moment is:

• A. $\frac{F}{2m}$
• B. $\frac{F-kx}{m}$
• C. $\frac{F-2kx}{m}$
• D. None of these

Answer 1

The correct option is C $\frac{F-2kx}{m}$

Writing Newton's second law for both blocks,
$Fnet=ma$
$F-kx=mb$ and $kx=ma$
Hence $m(b-a)=F-2kx$
$⟹(b-a)=\frac{F-2kx}{m}$
Ans (c)