List I describes four systems, each with two particles A and B in relative motion as shown in figures. List II gives possible magnitudes of their relative velocities $(i n m s^{- 1})$ at time $t = \frac{π}{3} s .$
Column – I
Column – II
A)
A and B are moving on a horizontal circle of radius 1m with uniform angular speed $ω = 1 r a d s^{- 1} .$ The initial angular positions of A and B (at time $t = 0$ ) $are θ = 0 and θ = \frac{π}{2}$ respectively, as shown.
P) $\frac{\sqrt{3} + 1}{2}$
B)
Projectiles A and B are fired (in the same vertical plane) at $t = 0 a n d t = 0.1 s$ respectively, with the same speed $v = \frac{5 π}{\sqrt{2}} m s^{- 1}$ and at $45 °$ from the horizontal plane. The initial separation between A and B is large enough so that they do not collide. $(g = 10 m s^{- 2}) .$
Q) $\frac{(\sqrt{3} - 1)}{\sqrt{2}}$
C)
Two simple harmonic oscillators A and B moving in the x direction according to $x_{A} = x_{0} \sin \frac{t}{t_{0}}$ and $x_{B} = x_{0} \sin (\frac{t}{t_{0}} + \frac{π}{2})$ respectively, starting from $t = 0.$ Take $x_{0} = 1 m, t_{0} = 1 s .$
R) $\sqrt{10}$
D)
Particle A is rotating in a horizontal circular path of radius 1m on the xy plane, with constant angular speed $ω = 1 r a d s^{- 1} .$ Particle B is moving up at a constant speed $3 m s^{- 1}$ in the vertical direction as shown in the figure. (Ignore gravity.)
S) $\sqrt{2}$
T) $\sqrt{25 π^{2} + 1}$
Which one of the following options is correct?

Question

List I describes four systems, each with two particles A and B in relative motion as shown in figures. List II gives possible magnitudes of their relative velocities $(i n m s^{- 1})$ at time $t = \frac{π}{3} s .$

Which one of the following options is correct?

Infinity Learn · Accepted Answer

A – R; B – T; C – P; D – S

Start JEE / NEET / Foundation preparation at rupees 99/day !!

Detailed Solution

Get Expert Academic Guidance – Connect with a Counselor Today!

Column – I		Column – II
A)	A and B are moving on a horizontal circle of radius 1m with uniform angular speed $ω = 1 r a d s^{- 1} .$ The initial angular positions of A and B (at time $t = 0$ ) $are θ = 0 and θ = \frac{π}{2}$ respectively, as shown.	P)	$\frac{\sqrt{3} + 1}{2}$
B)	Projectiles A and B are fired (in the same vertical plane) at $t = 0 a n d t = 0.1 s$ respectively, with the same speed $v = \frac{5 π}{\sqrt{2}} m s^{- 1}$ and at $45 °$ from the horizontal plane. The initial separation between A and B is large enough so that they do not collide. $(g = 10 m s^{- 2}) .$	Q)	$\frac{(\sqrt{3} - 1)}{\sqrt{2}}$
C)	Two simple harmonic oscillators A and B moving in the x direction according to $x_{A} = x_{0} \sin \frac{t}{t_{0}}$ and $x_{B} = x_{0} \sin (\frac{t}{t_{0}} + \frac{π}{2})$ respectively, starting from $t = 0.$ Take $x_{0} = 1 m, t_{0} = 1 s .$	R)	$\sqrt{10}$
D)	Particle A is rotating in a horizontal circular path of radius 1m on the xy plane, with constant angular speed $ω = 1 r a d s^{- 1} .$ Particle B is moving up at a constant speed $3 m s^{- 1}$ in the vertical direction as shown in the figure. (Ignore gravity.)	S)	$\sqrt{2}$
		T)	$\sqrt{25 π^{2} + 1}$