4. A plane composite object is made by attaching a thin uniform rod PQ of mass M, at right angles to the midpoint AB of a uniform rectangular lamina ABCD of mass m. Given that AB = Ga, BC = 3a = PQ, as shown in the diagram below: За B 3a D ба (i) Show that the moment of inertia I of the object about a smooth horizontal axist. through the midpoint of PQ and perpendicular to the plane of the lamina, is given by I = 4(17m + M)a² The object is slightly disturbed through small angles 0 from its equilibrium position to swing below Q. Aller time t, (ii) show that on = -3mga sin 0. dt?
4. A plane composite object is made by attaching a thin uniform rod PQ of mass M, at right angles to the midpoint AB of a uniform rectangular lamina ABCD of mass m. Given that AB = Ga, BC = 3a = PQ, as shown in the diagram below: За B 3a D ба (i) Show that the moment of inertia I of the object about a smooth horizontal axist. through the midpoint of PQ and perpendicular to the plane of the lamina, is given by I = 4(17m + M)a² The object is slightly disturbed through small angles 0 from its equilibrium position to swing below Q. Aller time t, (ii) show that on = -3mga sin 0. dt?
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Transcribed Image Text:A plane composite object is made by attaching a thin uniform rod PQ of mass M, at right angles to
the midpoint AB of a uniform rectangular lamina ABCD of mass m. Given that
4.
AB = 6a, BC = 3a = PQ,
as shown in the diagram below:
3a
A
B
3a
D'
ба
(i) Show that the moment of inertia I of the object about a smooth horizontal axis1, through the
midpoint of PQ and perpendicular to the plane of the lamina, is given by
I = (17m + M)a?
The object is slightly disturbed through small angles 0 from its equilibrium position to swing below Q.
Alter time t,
(ii) show that
-3mga sin 0.
dt?
(iii) find an expression for the period of small oscillations of the object about I.
(iv) show further that if m = M, then the component of the force perpendicular to the rod exerted by
ton co
the axis of rotation is mg sin 0.
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