An ideal spring with spring-constant $$k$$ is hung from the ceiling and a block of mass $$M$$ is attached to its lower end. The mass is released with the spring initially unstretched. Then the maximum extension in the spring is-
A.
$$\frac{{4Mg}}{k}$$
B.
$$\frac{{2Mg}}{k}$$
C.
$$\frac{{Mg}}{k}$$
D.
$$\frac{{Mg}}{2k}$$
Answer :
$$\frac{{2Mg}}{k}$$
Solution :
The above situation can also be looked upon as the decrease in the gravitational potential energy of spring mass system is equal to the gain in spring elastic potential energy.
$$Mgx = \frac{1}{2}k{r^2},\,\,\,x = \frac{{2Mg}}{k}$$
Releted MCQ Question on Basic Physics >> Work Energy and Power
Releted Question 1
If a machine is lubricated with oil-
A.
the mechanical advantage of the machine increases.
B.
the mechanical efficiency of the machine increases.
C.
both its mechanical advantage and efficiency increase.
D.
its efficiency increases, but its mechanical advantage decreases.
A particle of mass $$m$$ is moving in a circular path of constant radius $$r$$ such that its centripetal acceleration $${a_c}$$ is varying with time $$t$$ as $${a_c} = {k^2}r{t^2}$$ where $$k$$ is a constant. The power delivered to the particles by the force acting on it is:
A.
$$2\pi m{k^2}{r^2}t$$
B.
$$m{k^2}{r^2}t$$
C.
$$\frac{{\left( {m{k^4}{r^2}{t^5}} \right)}}{3}$$
A spring of force-constant $$k$$ is cut into two pieces such that one piece is double the length of the other. Then the long piece will have a force-constant of-