A particle starting from rest, moves in a circle of radius . It attains a velocity of m/s in the round. Its angular acceleration will be [2019]

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Q.
A particle starting from rest, moves in a circle of radius $' r'$ . It attains a velocity of $V_{0}$ m/s in the $n^{th}$ round. Its angular acceleration will be [2019]

1 $\frac{V_{0}}{n} {rad/s}^{2}$

2 $\frac{V_{0}}{2 π n r^{2}} {rad/s}^{2}$

3 $\frac{V_{0}^{2}}{4 π n r^{2}} {rad/s}^{2}$

4 $\frac{V_{0}^{2}}{4 π n r} {rad/s}^{2}$

Ans.
(3)

Distance travelled in $n^{th}$ rounds $= (2 π r) n$

Using $v^{2} = u^{2} + 2 a s$ or, $V_{0}^{2} = 0 + 2 a (2 π r) n \Rightarrow a = \frac{V_{0}^{2}}{4 π n r}$

Angular acceleration, $α = \frac{a}{r} = \frac{V_{0}^{2}}{4 π n r^{2}} {rad/s}^{2}$

Solution

Q.
A particle starting from rest, moves in a circle of radius $' r'$ . It attains a velocity of $V_{0}$ m/s in the $n^{th}$ round. Its angular acceleration will be [2019]

1 $\frac{V_{0}}{n} {rad/s}^{2}$

2 $\frac{V_{0}}{2 π n r^{2}} {rad/s}^{2}$

3 $\frac{V_{0}^{2}}{4 π n r^{2}} {rad/s}^{2}$

4 $\frac{V_{0}^{2}}{4 π n r} {rad/s}^{2}$

Ans.
(3)

Distance travelled in $n^{th}$ rounds $= (2 π r) n$

Using $v^{2} = u^{2} + 2 a s$ or, $V_{0}^{2} = 0 + 2 a (2 π r) n \Rightarrow a = \frac{V_{0}^{2}}{4 π n r}$

Angular acceleration, $α = \frac{a}{r} = \frac{V_{0}^{2}}{4 π n r^{2}} {rad/s}^{2}$

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Solution

Q. A particle starting from rest, moves in a circle of radius 'r'. It attains a velocity of V0 m/s in the nth round. Its angular acceleration will be [2019]

1 V0nrad/s2

2 V02πnr2rad/s2

3 V024πnr2rad/s2

4 V024πnrrad/s2

Ans. (3) Distance travelled in nth rounds =(2πr)n Using v2=u2+2as or, V02=0+2a(2πr)n⇒a=V024πnr Angular acceleration, α=ar=V024πnr2rad/s2

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Q.
A particle starting from rest, moves in a circle of radius $' r'$ . It attains a velocity of $V_{0}$ m/s in the $n^{th}$ round. Its angular acceleration will be [2019]

1 $\frac{V_{0}}{n} {rad/s}^{2}$

2 $\frac{V_{0}}{2 π n r^{2}} {rad/s}^{2}$

3 $\frac{V_{0}^{2}}{4 π n r^{2}} {rad/s}^{2}$

4 $\frac{V_{0}^{2}}{4 π n r} {rad/s}^{2}$

Ans.
(3)

Distance travelled in $n^{th}$ rounds $= (2 π r) n$

Using $v^{2} = u^{2} + 2 a s$ or, $V_{0}^{2} = 0 + 2 a (2 π r) n \Rightarrow a = \frac{V_{0}^{2}}{4 π n r}$

Angular acceleration, $α = \frac{a}{r} = \frac{V_{0}^{2}}{4 π n r^{2}} {rad/s}^{2}$