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CBSE-XI-Physics

05: Newton's Laws of Motion

with Solutions - page 3
Qstn# ii-12 Prvs-QstnNext-Qstn
  • #12
    In an imaginary atmosphere, the air exerts a small force F on any particle in the direction of the particle’s motion. A particle of mass m projected upward takes time t1 in reaching the maximum height and t2 in the return journey to the original point. Then
    (a) t1 < t2
    (b) t1 > t2
    (c) t1 = t2
    (d) the relation between t1 and t2 depends on the mass of the particle
    digAnsr:   b
    Ans : (b) t1 > t2
    Let acceleration due to air resistance force be a.
    Let H be maximum height attained by the particle.
    Direction of air resistance force is in the direction of motion.
    In the upward direction of motion, `` {a}_{\,\mathrm{\,eff \,}}=\left|g-a\right|``.
    `` {t}_{1}=\sqrt{\frac{2H}{\left|g-a\right|}}...\left(1\right)``
    In the downward direction of motion, `` {a}_{\,\mathrm{\,eff \,}}=g+a``.
    `` {t}_{2}=\sqrt{\frac{2H}{g+a}}...\left(2\right)``
    So, t1 > t2.