Question

Please answer this question!!​

Answer 1

Ans is d because if there is a lengthy dip then the body accelerates and reach the the end point quickly

Answer 2

☆ Let's understand the question.

》its given that the tracks are smooth(frictionless),means no energy loss, there is also no acceleration throughout their motion, so velocity will remain constant until the end.

》There is some reason for which the HINT is given, its make the ques simple and less complex.

》So let's first solve it by velocity/time graph!

☆Method-1 (V-T graph):

• $\rm velocity = \dfrac{displacement}{time}$

• and displacement is the shortest path between initial and final position.

• In the above image(attached) we can see, when the 2nd particle move from C to D its displacement covered will be equal to AB,i.e, x

• same it will happen to PQ and ST

• in total we can observe that displacement covered by both particles are same, and velocity is itself same at start of motion, so the time taken will also be same for both!

• There will be negligible effect of $\theta$ on velocity that will slightly change in the motion for 2nd particle, but there displacement is same covered ,

so the average of the velocity covered will be 'v',

thats why time is same!

☆see the graphs above.

☆Method 2 (by speed relation)

》see we can say that, disp. same everything same time same etc..

》But problem here arise, to properly visualise the qusetion. Like how when the speed is varying a little then they reach at the same time ? right?

》so, listen, when 2 one is moving from C to D its distance will be:

$\rm d = xcos\theta$

and the velocity responsible for moving in x-dirn:

$\rm v' = vcos\theta$

》$\rm speed_{CD} = \dfrac{d}{t}$

》$\rm t= \dfrac{xcos\theta}{vcos\theta}$

》$\bf t= x/v$-------☆

▪︎now this is same time taken by 1st one also in AB(x/v)

(same can be done for other dip in path)

》conclusion: The distance travelled is changed and velocity is also changed and together ther counter themselves by which the time remains same if we take path as straight also.

☆☆Both block reach at finish in same time.

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▪︎method 1st is quick and can be applied during Objective exams!!

▪︎merhod 2nd is easy to understand the concept of question!!

Hope you understand the solution!

Good luck : )