List of top Solid Mechanics Questions on Dynamics of rigid bodies under planar motion asked in GATE XE

An electric motor’s rotor is spinning at 1500 rpm when its load and power are cut off. The rotor, which has a mass of 50 kg and a radius of gyration of 200 mm, then coasts down to rest. Due to kinetic friction, a constant torque of 10 Nm acts on the rotor as it coasts down. The number of revolutions executed by the rotor before it comes to rest is .......... (in integer).

The figure shows a rod \(PQ\), hinged at \(P\), rotating counter-clockwise with angular speed \(\omega = 15 \, rad/s\). A block \(R\) translates along a slot cut in rod PQ. At the instant shown:
- Distance \(PR = 0.5 \, m\),
- \(\theta = 60^\circ\),
- Relative velocity of \(R\) with respect to PQ = 5 m/s,
- Relative acceleration of \(R\) with respect to PQ = 0.

Which one of the following is the CORRECT magnitude of the absolute acceleration (in m/s\(^2\)) of block R?

A slender elastic rod of length $1 \, m$, circular cross-section $d = 50 \, mm$, is subjected to equal and opposite end moments $M$. The midpoint lateral deflection is $10 \, mm$. Find maximum longitudinal strain in the rod, expressed as $p \times 10^{-3}$.

The state of stress at the critical location in a structure is \[ \sigma_{xx} = 420 \, MPa, \sigma_{yy} = 100 \, MPa, \sigma_{zz} = 0, \tau_{xy} = \tau_{yz} = \tau_{zx} = 0 \] The yield stress of the material in uniaxial tension is $400 \, MPa$. Select the correct statement among the following: