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NEET PHYSICSMedium

A body is thrown vertically upwards. If the air resistance is to be taken into account, then the time during which the body rises is:

A

Equal to the time of fall.

B

Less than the time of fall.

C

Greater than the time of fall.

D

Twice the time of fall.

Step-by-Step Solution

  1. Analyze Forces: Air resistance (fluid friction) always opposes the direction of motion (velocity) .
  2. Upward Motion (Ascent): The body moves upwards. Both gravity (mgmg) and air resistance (FairF_{air}) act downwards.
  • Net Force: Fnet=mg+FairF_{net} = mg + F_{air}.
  • Effective Retardation: aascent=g+Fairma_{ascent} = g + \frac{F_{air}}{m}.
  1. Downward Motion (Descent): The body moves downwards. Gravity (mgmg) acts downwards, while air resistance (FairF_{air}) acts upwards.
  • Net Force: Fnet=mg−FairF_{net} = mg - F_{air}.
  • Effective Acceleration: adescent=g−Fairma_{descent} = g - \frac{F_{air}}{m}.
  1. Conclusion: Since the magnitude of deceleration during ascent (g+aairg + a_{air}) is greater than the acceleration during descent (g−aairg - a_{air}), the body takes less time to cover the same distance during the upward journey than the downward journey. Therefore, tascent<tdescentt_{ascent} < t_{descent} .
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