A ball of mass $$2\,kg$$ and another of mass $$4\,kg$$ are dropped together from a $$60\,ft$$ tall building. After, a fall of $$30\,ft$$ each towards earth, their respective kinetic energies will be in the ratio of
A.
$$\sqrt 2 :1$$
B.
$$1:4$$
C.
$$1:2$$
D.
$$1:\sqrt 2 $$
Answer :
$$1:2$$
Solution :
Velocity of free falling body does not depend on its mass, it depends on the height from which it has been dropped.
$${v_1} = {v_2} = v$$ at a $$30\,ft$$ height from falling point.
Here, $${m_1} = 2\,kg,\,\,{m_2} = 4\,kg$$
Thus, $$\frac{{{K_1}}}{{{K_2}}} = \frac{{\frac{1}{2}{m_1}{v^2}}}{{\frac{1}{2}{m_2}{v^2}}} = \frac{{{m_1}}}{{{m_2}}} = \frac{2}{4} = \frac{1}{2}$$
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-