1.

Torques of equal magnitude are applied to a hollow cylinder and a solid sphere, both having the same mass and radius. The cylinder is free to rotate about its standard axis of symmetry, and the sphere is free to rotate about an axis passing through its centre. Which of the two will acquire a greater angular speed after a given time.

Answer» <html><body><p></p>Solution :Suppose `I_(1)andI_(2)` be the respective moment of inertia of hollow <a href="https://interviewquestions.tuteehub.com/tag/cylinder-942617" style="font-weight:bold;" target="_blank" title="Click to know more about CYLINDER">CYLINDER</a> and the solid sphere and `omega_(1)andomega_(2)` be the respective <a href="https://interviewquestions.tuteehub.com/tag/angular-11524" style="font-weight:bold;" target="_blank" title="Click to know more about ANGULAR">ANGULAR</a> <a href="https://interviewquestions.tuteehub.com/tag/velocity-1444512" style="font-weight:bold;" target="_blank" title="Click to know more about VELOCITY">VELOCITY</a> and `alpha_(1)andalpha_(2)` respective angular accelerations. <br/> As can equal torque is applied to both the bodies <br/> `I_(1)alpha_(1)=I_(2)alpha_(2)` <br/> `:. (I_(1))/(I_(2))=(alpha_(2))/(alpha_(1))` <br/> but `(MR^(2))/((2)/(5)MR^(2))=(alpha_(2))/(alpha_(1))` <br/> `:.(5)/(2)=(alpha_(2))/(alpha_(1)).....(1)` <br/> Now in `omega=omega_(0)+alphat,omega_(0)=0` <br/> `omega_(1)=alpha_(1)tandomega_(2)=alpha_(2)t` <br/> `:. (omega_(1))/(omega_(2))=(alpha_(1))/(alpha_(2)).....(2)` <br/> `:. (omega_(1))/(omega_(2))=(2)/(5)` [From <a href="https://interviewquestions.tuteehub.com/tag/eqn-973463" style="font-weight:bold;" target="_blank" title="Click to know more about EQN">EQN</a>. (1)] <br/> `:. omega_(2)gtomega_(1)` <br/> `:.` The angular speed of the solid sphere will be greater than that of hollow cylinder.</body></html>


Discussion

No Comment Found

Related InterviewSolutions