A) \[\frac{{{m}_{1}}}{{{m}_{2}}}\]
B) \[\frac{{{m}_{2}}}{{{m}_{1}}}\]
C) \[1\]
D) \[\frac{\sqrt{{{m}_{1}}{{m}_{2}}}}{{{m}_{1}}+{{m}_{2}}}\]
Correct Answer: B
Solution :
: The acceleration of the body of mass \[{{m}_{1}}\] acts upon by a constant F is \[{{a}_{1}}=\frac{F}{{{m}_{1}}}\] ??.(i) The acceleration of the body of mass \[{{m}_{2}}\] acts upon by a same constant F is \[{{a}_{2}}=\frac{F}{{{m}_{2}}}\] ???(ii) Starting from rest, the velocity acquired by mass \[{{m}_{2}}\] in time t is \[{{\upsilon }_{1}}={{a}_{1}}t=\frac{F}{{{m}_{1}}}t\] (Using (i)) ??(iii) Starting from rest, the velocity acquired by mass \[{{m}_{2}}\] in the same time t is \[{{\upsilon }_{2}}={{a}_{2}}t=\frac{F}{{{m}_{2}}}t\](Using (ii)) ??.(iv) Divide (iii) by (iv), we get \[\therefore \] \[\frac{{{\upsilon }_{1}}}{{{\upsilon }_{2}}}=\frac{{{m}_{2}}}{{{m}_{1}}}\] ???.(v) Kinetic energy of mass \[{{m}_{1}}\] is \[{{E}_{1}}=\frac{1}{2}{{m}_{1}}\upsilon _{1}^{2}\] ???(vi) Kinetic energy of mass \[{{m}_{2}}\] is \[{{E}_{2}}=\frac{1}{2}{{n}_{2}}\upsilon _{2}^{2}\] ??.(vii) Divide (vi) by (vii), we get \[\frac{{{E}_{1}}}{{{E}_{2}}}=\frac{{{m}_{1}}}{{{m}_{2}}}{{\left( \frac{{{\upsilon }_{1}}}{{{\upsilon }_{2}}} \right)}^{2}}\] \[=\frac{{{m}_{1}}}{{{m}_{2}}}{{\left( \frac{{{m}_{2}}}{{{m}_{1}}} \right)}^{2}}\](Using (v)) \[=\frac{{{m}_{1}}}{{{m}_{2}}}\]
You need to login to perform this action.
You will be redirected in
3 sec
