AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

In the List-I below, four different paths of a particle are given as functions of time. In these functions, $α a n d β$ are positive constants of appropriate dimensions and $α \neq β$ . In each case, the force acting on the particle is either zero or conservative. In List-II. Certain statements are given about speed and angular velocity of the particle about origin. Match each path in List-I with those quantities in List-II.
List-I
List-II
(P)
$\vec{r} (t) = α t \hat{i} + β t j$
(1)
Speed is constant
(Q)
$\vec{r} (t) = α (\cos ω t \hat{i} + \sin ω t j)$
(2)
Speed is decreasing with time
(R)
$\vec{r} (t) = α \hat{i} + β t j$
(3)
Speed is increasing with time
(S)
$\vec{r} (t) = α t \hat{i} + \frac{β}{2} t^{2} j$
(4)
Angular velocity is constant

(5)
Angular velocity is decreasing with time

(6)
Angular velocity is increasing with time

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

$(P) - (2, 4), (Q) - (3, 5), (R) - (1, 4), (S) - (2, 5)$

$(P) - (3, 5), (Q) - (2, 5), (R) - (2, 4), (S) - (2, 5)$

$(P) - (1, 4), (Q) - (1, 4), (R) - (1, 5), (S) - (3, 5)$

$(P) - (1, 5), (Q) - (2, 5), (R) - (3, 4), (S) - (5)$

answer is B.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

(P) $\vec{v} = α \hat{i} + β j$
Speed is constant. Particle moves in straight line passing through origin, $ω = 0$ always.
(Q) Uniform circular motion both v and v and $ω$ are constant.
(S) $x = α t, y = \frac{β t^{2}}{2}$
Question Image

$y = \frac{β}{2 α^{2}} x^{2} \to p a r a b o l i c p a t h \vec{v} = α \hat{i} + β t j \to s p e e d i s i n c r e a \sin g ω = \frac{d α}{d t} \tan γ = \frac{y}{x} = \frac{β t}{2 α} \sec^{2} γ \frac{d α}{d t} = \frac{β}{2 α} ω = \frac{β}{2 α} \cos^{2} γ = \frac{2 β α}{\sqrt{β^{2} γ^{2} + 4 α^{2}}}$

$ω$ decreases with time.
(R) $\vec{v} = β j$
Question Image
$\tan γ = \frac{y}{x} = \frac{β t}{α} \sec^{2} γ \frac{d x}{d t} = \frac{β}{α} ω = \frac{β}{α} \cos^{2} γ = \frac{β}{\sqrt{α^{2} + β^{2} t^{2}}}$

$ω$ decreases with time.

Watch 3-min video & get full concept clarity

courses

No courses found

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Get Expert Academic Guidance – Connect with a Counselor Today!