TS EAMCET · Physics · Center of Mass Momentum and Collision

A bullet of mass $m$ moving horizontally with speed $v_{0}$ hits a wooden block of mass $M$ that is suspended from a massless string. The bullet gets lodged into the block and comes into halt. If the block-bullet combine swings to a maximum height $h$ then how much of the initial kinetic energy of the bullet is lost in the collision?

A $\frac{1}{2} m v_{0}^{2} (\frac{M}{m + M})$
B $\frac{1}{2} m v_{0}^{2} (\frac{M + m}{M})$
C $\frac{1}{2} m v_{0}^{2} (\frac{M^{2}}{(m + M)^{2}})$
D $\frac{1}{2} m v_{0}^{2} (\frac{{(M + m)}^{2}}{M^{2}})$

Verified Solution

Answer & Solution

Correct Answer

(A) $\frac{1}{2} m v_{0}^{2} (\frac{M}{m + M})$

Step-by-step Solution

Detailed explanation

Given: Mass of bullet m, the velocity of bullet v0 and mass of the wooden block M. Let the velocity of the bullet after the collision with the wooden block be v Applying the law of conservation of momentum, we obtain mv0=M+mv v=mv0M+m Now applying the law of conservation of…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Explore more questions on app

From TS EAMCET

Explore more questions on app