A solid sphere of mass M and radius R is placed on a smooth horizontal surface. It is given a horizontal impulse J at a height h above the centre of mass and sphere starts rolling then, the value of h and speed of centre of mass are - |
A) \[h=\frac{2}{3}R\] and \[v=\frac{J}{M}\]
B) \[h=\frac{2}{5}R\] and \[v=\frac{2}{5}\frac{J}{M}\]
C) \[h=\frac{7}{5}R\] and \[v=\frac{7}{5}\frac{J}{M}\]
D) \[h=\frac{7}{5}R\] and \[v=\frac{J}{M}\]
Correct Answer: A
Solution :
Let the force producing impulse J is F then |
\[{{\tau }_{about}}C=I\alpha \] |
\[\tau \] and \[F=M\alpha \] (where a= R\[\alpha \]) |
\[\therefore \,\,\,M\alpha h=\frac{2}{5}MRa\] \[\Rightarrow h=\frac{2}{5}R\] |
Also impulse = change in momentum |
Or \[J=Mv\] |
\[\therefore \,\,\,\,\,\,\,v=\frac{J}{M}\] |
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