Question

Q. A block of mass m is sliding on a fixed smooth inclined plane of angle $\theta$ = 30° in case (I). In case (Il) inclined plane is accelerated horizontally so that the block does not slide with respect to it. Then what is the ratio of acceleration of the block in horizontal direction in two cases?​

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Answer 1

In first case

In first caseobject is sliding on plane

it's acceration(horizontal+vertical)=gsin∅

now, breaking this acceleration in horizontal and vertical part(as shown in figureiii),we will get

horizontal acceleration=gsin∅cos∅

In second case,

the block block is stationery on inclined plane,due to acceleration a of the inclined plane which created a psuedo force in opposite direction....

Pseudo,accleration =opposite direction of acceleration of plane..

breaking this acceleration (as shown in figure,iv)

we can say

a0cos∅-gsin∅=0. (a0cos∅, makes the resulant acceleration 0,by accting in opposite direction,of accleration during sliding)

a0cos∅=gsin∅

a0=gtan∅

Also,since the plane is moving with acceleration a0 in horizontal direction,so the block will also,move with it in the same direction...

Horizontal acceleration in second case=a0=gtan∅

now,

their ratio=(gsin∅cos∅)/gtan∅ =cos^2∅=cos^2(30°)

=3/4

{hope it helps}

Answer 2

Answer:

Explanation:

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