Respected Sir /Mam
This question is from previous year and not from above mentioned topics.
 
 
Q.  A body of mass m moving with  a velocity v in the x- direction collides with another body of mass      M moving in the y-direction with a velocity V. They form one  body during collision. The direction          of the momentum of the composite body with x- axis is
Options--
 
A) tan inverse 1 (mV/Mv)
B)tan inverse 1 ( MV/mv)
C) tan inverse 1 (M/M+m)
D) tan innverse 1 ( M+m/M)

Asked by Kb Aulakh | 27th Apr, 2015, 11:32: PM

Expert Answer:

Consider that a body of mass 'm' moving with velocity 'v' along x- axis collides with body of mass 'M' moving with velocity 'V' along y axis as shown in the figure below.
Let v' be the velocity of the composite body with x axis.


Conservation of x component of momentum can be written as:
mv =  (m+V) v' cos θ  -------------(1)
Conservation of y component of momentum can be written as:
MV =  (m+V) v' sin θ  -------------(2)
Dividing (2) by (1) we get that:
 
begin mathsize 12px style MV over mv equals fraction numerator left parenthesis straight m plus straight V right parenthesis space straight v apostrophe space sin space straight theta over denominator left parenthesis straight m plus straight V right parenthesis space straight v apostrophe space cos space straight theta space end fraction MV over mv equals tan space straight theta rightwards double arrow space straight theta space equals space tan to the power of negative 1 end exponent open parentheses MV over mv close parentheses end style
 
 
 
 
 
 
 

Answered by Jyothi Nair | 28th Apr, 2015, 10:45: AM