Verified Solution • 2025–26 Session moderate

QJEEM21Ph734a: JEE Main 2021 Physics - Class 11 JEEM21Ph734a Solution: A large block of wood of mass M = 5.99 kg is hanging from two…

A large block of wood of mass M = 5.99 kg is hanging from two long massless cords. A bullet of mass m = 10 g is fired into the block and gets embedded in it. The (block + bullet) then swing upwards, their centre of mass rising a vertical distance h = 9.8 cm before the (block + bullet) pendulum comes momentarily to rest at the end of its arc. The speed of the bullet just before collision is :
(take g = 9.8 ms-2)

JEE Main 2021 (Online) 16th March Evening Shift Physics - Center of Mass and Collision Question 57 English

Multiple Choice Options

  • A 831.4 m/s
  • B 811.4 m/s
  • C 841.4 m/s
  • D 821.4 m/s

Step-by-Step Verified Solution

Pi=0.01×u+0=Pf=6×v{P_i} = 0.01 \times u + 0 = {P_f} = 6 \times v

v=0.01u6v = {{0.01u} \over 6}

using energy conservation

12×6×(u600)2=6×9.8×9.8×10−2{1 \over 2} \times 6 \times {\left( {{u \over {600}}} \right)^2} = 6 \times 9.8 \times 9.8 \times {10^{ - 2}}

⇒\Rightarrow u=6×98×2=5882u = 6 \times 98 \times \sqrt 2 = 588\sqrt 2 m/s

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