A circular disc of moment of inertia $I_t$, is rotating in a horizontal plane, about its symmetry axis, with a constant angular speed $\omega_i$ . Another disc of moment of inertia $l_b$ is dropped coaxially onto the rotating disc. Initially the second disc has zero angular speed. Eventually both the discs rotate with a constant angular speed $\omega_f$. The energy lost by the initially rotating disc to friction is
A circular disc of moment of inertia $I_t$, is rotating in a horizontal plane, about its symmetry axis, with a constant angular speed $\omega_i$ . Another disc of moment of inertia $l_b$ is dropped coaxially onto the rotating disc. Initially the second disc has zero angular speed. Eventually both the discs rotate with a constant angular speed $\omega_f$. The energy lost by the initially rotating disc to friction is
- [AIPMT 2010]
- A
$\frac{1}{2}\;\frac{{{I_b}^2}}{{\left( {{I_t} + {I_b}} \right)}}{\omega _i}^2$
- B
$\;\frac{1}{2}\;\frac{{{I_t}^2}}{{\left( {{I_t} + {I_b}} \right)}}{\omega _i}^2$
- C
$\;\frac{1}{2}\;\frac{{\left( {{I_b} - {I_t}} \right)}}{{\left( {{I_t} + {I_b}} \right)}}{\omega _i}^2$
- D
$\;\frac{1}{2}\;\frac{{{I_b}{I_t}}}{{\left( {{I_t} + {I_b}} \right)}}{\omega _i}^2$
Similar Questions
A thin and uniform rod of mass $M$ and length $L$ is held vertical on a floor with large friction. The rod is released from rest so that it falls by rotating about its contact-point with the floor without slipping. Which of the following statement($s$) is/are correct, when the rod makes an angle $60^{\circ}$ with vertical ? [ $g$ is the acceleration due to gravity]
$(1)$ The radial acceleration of the rod's center of mass will be $\frac{3 g }{4}$
$(2)$ The angular acceleration of the rod will be $\frac{2 g }{ L }$
$(3)$ The angular speed of the rod will be $\sqrt{\frac{3 g}{2 L}}$
$(4)$ The normal reaction force from the floor on the rod will be $\frac{ Mg }{16}$
A thin and uniform rod of mass $M$ and length $L$ is held vertical on a floor with large friction. The rod is released from rest so that it falls by rotating about its contact-point with the floor without slipping. Which of the following statement($s$) is/are correct, when the rod makes an angle $60^{\circ}$ with vertical ? [ $g$ is the acceleration due to gravity]
$(1)$ The radial acceleration of the rod's center of mass will be $\frac{3 g }{4}$
$(2)$ The angular acceleration of the rod will be $\frac{2 g }{ L }$
$(3)$ The angular speed of the rod will be $\sqrt{\frac{3 g}{2 L}}$
$(4)$ The normal reaction force from the floor on the rod will be $\frac{ Mg }{16}$
- [IIT 2019]
$A$ rod hinged at one end is released from the horizontal position as shown in the figure. When it becomes vertical its lower half separates without exerting any reaction at the breaking point. Then the maximum angle $‘\theta ’$ made by the hinged upper half with the vertical is ......... $^o$.
$A$ rod hinged at one end is released from the horizontal position as shown in the figure. When it becomes vertical its lower half separates without exerting any reaction at the breaking point. Then the maximum angle $‘\theta ’$ made by the hinged upper half with the vertical is ......... $^o$.
A solid cylinder of mass $20 \;kg$ rotates about its axis with angular speed $100\; rad s ^{-1}$ The radius of the cylinder is $0.25 \;m$. What is the kinetic energy associated with the rotation of the cylinder? What is the magnitude of angular momentum of the cylinder about its axis?
A solid cylinder of mass $20 \;kg$ rotates about its axis with angular speed $100\; rad s ^{-1}$ The radius of the cylinder is $0.25 \;m$. What is the kinetic energy associated with the rotation of the cylinder? What is the magnitude of angular momentum of the cylinder about its axis?
For the pivoted slender rod of length $l$ as shown in figure, the angular velocity as the bar reaches the vertical position after being released in the horizontal position is
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- [NEET 2016]