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NEET PHYSICSMedium

The velocity of a bullet is reduced from 200 m/s200 \text{ m/s} to 100 m/s100 \text{ m/s} while travelling through a wooden block of thickness 10 cm10 \text{ cm}. The retardation, assuming it to be uniform, will be:

A

10×104 m/s210 \times 10^4 \text{ m/s}^2

B

12×104 m/s212 \times 10^4 \text{ m/s}^2

C

13.5×104 m/s213.5 \times 10^4 \text{ m/s}^2

D

15×104 m/s215 \times 10^4 \text{ m/s}^2

Step-by-Step Solution

  1. Identify Given Values: Initial velocity, u=200 m/su = 200 \text{ m/s}. Final velocity, v=100 m/sv = 100 \text{ m/s}.
  • Displacement (thickness), s=10 cm=0.1 ms = 10 \text{ cm} = 0.1 \text{ m} (Note: Unit conversion is crucial).
  1. Select Formula: Use the kinematic equation relating velocity, acceleration, and displacement: v2=u2+2asv^2 = u^2 + 2as .
  2. Calculation: (100)2=(200)2+2a(0.1)(100)^2 = (200)^2 + 2a(0.1) 10000=40000+0.2a10000 = 40000 + 0.2a 0.2a=10000−400000.2a = 10000 - 40000 0.2a=−300000.2a = -30000 a=−300000.2=−150000 m/s2a = \frac{-30000}{0.2} = -150000 \text{ m/s}^2.
  3. Scientific Notation: Magnitude of acceleration (retardation) =150000 m/s2=15×104 m/s2= 150000 \text{ m/s}^2 = 15 \times 10^4 \text{ m/s}^2.
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