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Newton’s Laws of Motion — Physics STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 SciencePhysicsNewton’s Laws of Motion5 Marks
Question
Two objects A and B are thrown upward simultaneously with the same speed. The mass of A is greater than the mass of B. Suppose the air exerts a constant and equal force of resistance on the two bodies:
  1. The two bodies will reach the same height.
  2. A will go higher than B.
  3. B will go higher than A.
  4. Any of the above three may happen depending on the speed with which the objects are thrown.
✓

Answer

  1. A will go higher than B.
Explanation:

Let the air exert a constant resistance force = F (in downward direction).

Acceleration of particle A in downward direction due to air resistance, $\text{a}_{\text{A}}=\frac{\text{F}}{\text{m}_{\text{A}}}.$

Acceleration of particle B in downward direction due to air resistance, $\text{a}_{\text{B}}=\frac{\text{F}}{\text{m}_{\text{B}}}.$

$\text{m}_{\text{A}}>\text{m}_{\text{B}}$

$\text{a}_{\text{A}}<\text{a}_{\text{B}}$

$\text{S = us}+\frac{1}2{}\text{at}^2$

So, $\text{H}_{\text{A}}=\text{ut}-\frac{1}{2}\big(\text{a}_{\text{A}}+\text{g}\big)\text{t}^2$

$\text{H}_{\text{B}}=\text{ut}-\frac{1}{2}\big(\text{a}_{\text{B}}+\text{g}\big)\text{t}^2$

$\text{H}_{\text{A}}>\text{H}_{\text{B}}$

Therefore, A will go higher than B.

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