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Work and Energy — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsWork and Energy1 Mark
MCQ
A heavy stone is thrown in from a cliff of height h in a given direction. The speed with which it hits the ground:
  • A
    Must depend on the speed of projection.
  • B
    Must be larger than the speed of projectio.
  • C
    Must be independent of the speed of projection.
  • ✓
    Both $A$ and $B.$
✓

Answer

Correct option: D.
Both $A$ and $B.$
Consider that the stone is projected with initial speed $v.$
As the stone is falls under the gravitational force, which is a conservative force, the total energy of the stone remains the same at every point during its motion.
From the conservation of energy, we have:
Initial energy of the stone = final energy of the stone
i.e., $(K.E.)_i + (P.E.)_i= (K.E.)_f+ (P.E.)_f$
$=\frac{1}{2}\text{mv}_\text{r}^2+\text{mgh}=\frac{1}{2}\text{m}(\text{v}_\text{max})^2$
$\Rightarrow\text{v}_\text{max}=\sqrt{\text{v}^2+2\text{gh}}$
From the above expression, we can say that the maximum speed with which the stone hits the ground depends on the speed of projection and greater than it.

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