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Question
Two objects A and B are thrown upward simultaneously with the same speed. The mass of A is greater than that of B. Suppose the air exerts a constant and equal force of resistance on the two bodies.
Options
The two bodies will reach the same height.
A will go higher than B.
B will go higher than A.
Any of the above three may happen depending on the speed with which the objects are thrown.
Solution
A will go higher than B.
Let the air exert a constant resistance force = F (in downward direction).
Acceleration of particle A in downward direction due to air resistance, aA = F/mA.
Acceleration of particle B in downward direction due to air resistance, aB = F/mB.
mA > mB
aA < aB
\[S = ut + \frac{1}{2}a t^2\]
\[So, H_A = ut - \frac{1}{2}( a_A + g) t^2\]
\[H_B = ut - \frac{1}{2}( a_B + g) t^2\]
\[H_A > H_B\]
Therefore, A will go higher than B.
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