    Question

# A bullet of mass 50 g is fired from below into the bob of mass 450 g of a long simple pendulum, as shown in the figure. The bullet remains inside the bob and bob rises through a height of 1.8 m. Find the speed of the bullet. [Take g=10 ms−2] A
60 ms1
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B
180 ms1
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C
36.6 ms1
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D
60 ms1
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Solution

## The correct option is D 60 ms−1Given, mbob=0.45 kg ; mbullet=0.05 kg h=1.8 m In collision, there is no external force involved. Thus, linear momentum of the system will be conserved. Let initial velocity of the bullet and final velocity of (bob+bullet ) be v and V respectively. ∴ Pi=Pf (0.05×v)+(0.45×0)=(0.05+0.450)×V 0.05v=0.5V ∴ V=v10 After collision, the system of (bob+pullet) rises to a height of 1.8 m. Using kinematic equations, v2=u2+2as Here, v=0; u=V; a=−g; h=1.8 m (0)2=(V)2+[2(−10)×(1.8)] ⇒V2=2×10×1.8 ⇒(v10)2=36 ∴v=60 ms−1 <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, (D) is the correct answer.  Suggest Corrections  0      Similar questions  Explore more