JEE Main & Advanced Physics Motion in a Straight Line / सरल रेखा में गति Question Bank Topic Test - One Dimensional Motion

  • question_answer
    The velocity v and position r of a body are related as, \[{{v}^{2}}=kr,\] where k is a constant. What will be the velocity after 1 second? Given that the position is zero at \[t=0\].

    A) \[\sqrt{kr}\]

    B) \[k{{r}^{-3/2}}\]

    C) \[\frac{k}{2}{{r}^{0}}\]                 

    D) cannot be determined from the given information

    Correct Answer: C

    Solution :

    [c] \[{{\upsilon }^{2}}=kr\]
    \[\Rightarrow \]            \[2\upsilon \frac{d\upsilon }{dt}=k\frac{dr}{dt}\]
    \[\Rightarrow \]            \[\frac{d\upsilon }{dt}=\frac{k}{2}\]
    \[\Rightarrow \]            \[{{\upsilon }_{2}}-{{\upsilon }_{1}}=\frac{k}{2}({{t}_{2}}-{{t}_{1}})\]
    \[\upsilon =\frac{k}{2}\]


You need to login to perform this action.
You will be redirected in 3 sec spinner