question_answer

                In an experiment, a small steel ball falls through a liquid at a constant speed of 10cm/s. If the steel ball is pulled upward with a force equal to twice its effective weight, how fast will it move upward?     JEE Main Online Paper ( Held On 25  April 2013 )

A)                 5 cm/s                  

B)                                        Zero

C)                                        10 cm/s               

D)                                        (d) 20 cm/s

Correct Answer: C

Solution :

                              Weight of the body \[W=mg=\frac{4}{3}\pi {{r}^{3}}\rho g\] \[T=\frac{4}{3}\pi {{r}^{3}}\sigma g\]and\[F=6\pi \eta vt\] When the body attains terminal velocity net force acting on the body is zero. i.e., W-T-F=0 And terminal velocity\[v=\frac{2}{9}\frac{{{r}^{2}}(\rho -\sigma )g}{\eta }\] As in case of upward motion upward force is twice its effective weight, therefore, it will move with same speed 10 cm/s