2. Questions Bank
  3. JEE Main & Advanced
  4. Physics
  5. Rotational Motion

JEE Main & Advanced Physics Rotational Motion Question Bank Mock Test - Dynamics of Rigid Body

  • question_answer
    A pulley of radius 2 m is rotated about its axis by a force \[F=(20t-5{{t}^{2}})\] newton (where \[t\] is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is \[10\,kg{{m}^{2}}\], the number of rotations made by the pulley before its direction of motion is reversed, is:

    A) less than 3

    B) more than 3 but less than 6

    C) more than 6 but less than 9

    D) more than 9

    Correct Answer: B

    Solution :

    [b] \[\tau =(20t-5{{t}^{2}})2=40t-10{{t}^{2}}\] \[\alpha =\frac{\tau }{I}=\frac{40t-10{{t}^{2}}}{10}=4t-{{t}^{2}}\] \[\omega =\int\limits_{0}^{t}{\alpha dt}=2{{t}^{2}},-\frac{{{t}^{3}}}{3}\] When direction is reversed, co is zero. So \[2{{t}^{2}}-\frac{{{t}^{3}}}{3}=0\Rightarrow {{t}^{3}}=6{{t}^{2}}\Rightarrow t=6s\] \[\theta =\int{\omega dt}\] \[=\int\limits_{0}^{6}{(2{{t}^{2}}-\frac{{{t}^{3}}}{3})dt}\] \[={{\left[ \frac{2{{t}^{2}}}{3}-\frac{{{t}^{4}}}{12} \right]}^{6}}_{0}=36rad\] Number of revolution = \[\frac{36}{2\pi }\] = Less than 6


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