Question

Each situation in column I gives graph of a particle moving in circular path. The variables and t represent angular speed (at any time t ), angular displacement (in time t) and time respectively. Column II gives certain resulting interpretation. Match the graphs in column I with statements in column II.

• A. P→3,Q→2,R→3,S→4
• B. P→2,Q→3,R→4,S→1
• C. P→2,Q→1,R→1,S→2
• D. P→4,Q→3,R→3,S→2

Answer 1

The correct option is C

P→2,Q→1,R→1,S→2

From graph (a) $\Rightarrow \omega =k\theta$ where k is positive constant

• angular acceleration

$=\omega \frac{d\omega }{d\theta }=k\theta \times k=k^2\theta$

angular acceleration is non uniform and directly proportional to $\theta$

From graph (b) $\Rightarrow {\omega }^2=k\theta$ Differentiating both sides with respect to $\theta$

$2\omega \frac{d\omega }{d\theta }=kor\omega \frac{d\omega }{d\theta }=\frac{k}{2}$ Hence angular acceleration is uniform.

From graph (c) $\Rightarrow \omega =kt$

angular acceleration $=\frac{dw}{dt}=k$ Hence angular acceleration is uniform

From graph (d) $\Rightarrow \omega =k{t}^2$

angular acceleration $=\frac{d\omega }{dt}=2kt$

Hence angular acceleration is non uniform and directly proportional to t.