Kinematics of Circular Motion questions | Kinematics of Circular Motion jee questions

1

2

3

4

(C) Given : R = 9m and 120 revolutions in 3 min

Angular velocity, $ω = \frac{120 R e v .}{3 m i n .} = \frac{120 \times 2 π r a d}{3 \times 60 s e c} = \frac{4 π}{3} r a d / s$

$a_{c e n t r i p e t a l} = ω^{2} R = {(\frac{4 π}{3})}^{2} \times 9 = 16 π^{2} m / s^{2}$

1

2

3

4

(C) $x_{m i n} = π \times r_{m i n} = π \times \frac{60}{100} m .$

$x_{s e c o n d} = 30 \times 2 π \times r_{s e c o n d} = 30 \times 2 π \times \frac{75}{100}$

$x = x_{s e c o n d} - x_{m i n} = 139.4 m$

(8) $| {\vec{a}}_{c} | = | {\vec{a}}_{t} |$

$\frac{v^{2}}{r} = \frac{d v}{d t} \Rightarrow \int_{4}^{v} \frac{d v}{v^{2}} = \int_{0}^{t} \frac{d t}{r}$

$\Rightarrow {[\frac{- 1}{v}]}_{4}^{v} = \frac{t}{r} \Rightarrow \frac{- 1}{v} + \frac{1}{4} = 2 t$

$\Rightarrow v = \frac{4}{1 - 8 t} = \frac{d s}{d t}$

$4 \int_{0}^{t} \frac{d t}{1 - 8 t} = \int_{0}^{s} d s$

$(r = 0.5 m s = 2 π r = π)$

$4 \times \frac{{[l n (1 - 8 t)]}_{0}^{t}}{- 8} = π$

$l \ln (1 - 8 t) = - 2 π$

$1 - 8 t = e^{- 2 π} \Rightarrow t = \frac{1}{8} (1 - e^{- 2 π})$

$S o, α = 8$

Want Us to Email you About Special Offers & Updates?