Circular MotionHardBloom L1
Question
A particle is in motion on the x-axis. The variation of its velocity with position is as shown. The graph is circle and its equation is x2 + v2 =1, where x is in m and v in m/s. The CORRECT statement(s) is/are
Options
A.When x is positive, acceleration is negative.
B.When x is negative, acceleration is positive.
C.At Q, acceleration has magnitude $\frac{1}{\sqrt{2}}$m/s2
D.At S, acceleration is infinite.
Solution
Sol. x2 + v2 = 1
⇒ $2x + 2v\frac{dv}{dx} = 0$
⇒ $v\frac{dv}{dx} = - \overrightarrow{x} = \overrightarrow{a}$
⇒ $Q\left( \frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}} \right)$ ⇒ xQ = $\frac{1}{\sqrt{2}} \Rightarrow |a| = \frac{1}{\sqrt{2}}$
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