IIT-JEE 2008 · Paper 1 · Physics Q30

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PhysicsMultiple correct+4 / -1Question 30 of 69

Two balls, having linear momenta $\vec p_1=p\hat i$ and $\vec p_2=-p\hat i$ , undergo a collision in free space. There is no external force acting on the balls. Let $\vec p_1'$ and $\vec p_2'$ be their final momenta. The following option(s) is(are) NOT ALLOWED for any non-zero value of $p,a_1,a_2,b_1,b_2,c_1$ and $c_2$ .

\vec p_1'=a_1\hat i+b_1\hat j+c_1\hat k

\vec p_2'=a_2\hat i+b_2\hat j

\vec p_1'=c_1\hat k

\vec p_2'=c_2\hat k

\vec p_1'=a_1\hat i+b_1\hat j+c_1\hat k

\vec p_2'=a_2\hat i+b_2\hat j-c_1\hat k

\vec p_1'=a_1\hat i+b_1\hat j

\vec p_2'=a_2\hat i+b_1\hat j

Answer and worked solution

Official answer: A, D

Momentum conservation. The initial total momentum is zero, so $\vec p_1'+\vec p_2'=0$ in every component.

(A) The $\hat k$ components are $c_1$ and 0: total $c_1\ne0$ . Not allowed.
(B) $c_1+c_2=0$ is possible. Allowed.
(C) $\hat k$ components cancel, and $a_1+a_2=0$ , $b_1+b_2=0$ are possible. Allowed.
(D) The $\hat j$ components are $b_1+b_1=2b_1\ne0$ . Not allowed.

(A), (D)

Topics:Conservation of linear momentum

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IIT-JEE 2008 · Paper 1, Physics question 30