Figure shows a lamina in $$x y$$-plane. Two axes $$z$$ and $$z^{\prime}$$ pass perpendicular to its plane. A force $$\mathbf{F}$$ acts in the plane of lamina at point $$P$$ as shown. Which of the following are true? (The point $$P$$ is closer to $$z^{\prime}$$-axis than the $$z$$-axis.)
With reference to figure of a cube of edge $$a$$ and mass $$m$$, state whether the following are true or false. (0 is the centre of the cube.)
The centre of gravity of a body on the earth coincides with its centre of mass for a small object whereas for an extended object it may not. What is the qualitative meaning of small and extended in this regard? For which of the following two coincides? A building, a pond, a lake, a mountain?
When the vertical height of the object is very small as compared to the earth's radius, we call the object small, otherwise it is extended.
(i) Building and pond are small objects.
(ii) A deep lake and a mountain are examples of extended objects.
Why does a solid sphere have smaller moment of inertia than a hollow cylinder of same mass and radius, about an axis passing through their axes of symmetry?
The moment of inertia of a body is given by $$I=\Sigma m_i r_i^2$$ [sum of moment of inertia of each constituent particles]
All the mass in a cylinder lies at distance $$R$$ from the axis of symmetry but most of the mass of a solid sphere lies at a smaller distance than $$R$$.
The variation of angular position $$\theta$$, of a point on a rotating rigid body, with time $$t$$ is shown in figure. Is the body rotating clockwise or anti-clockwise?
As the slope of $$\theta$$-t graph is positive and positive slope indicates anti-clockwise rotation which is traditionally taken as positive.