NTSE Stage 2 SAT 2019 Exam Question Paper

Question : 64 of 100

Marks: +1, -0

Two cars 'A' and ‘B’ of same mass start from the same location at the same time out on different straight roads. Car 'A' travels on a road that has greater angle of inclination with horizontal compared to the road on which 'B' Travels.
At any instant both cars 'A ’ and ‘B’ have the same height above the starting point. If

E_A

and

E_B

are total energies of cars ‘A* and 'B ' respectively, then

$E_A < E_B$
$E_A=E_B$
$E_A > E_B$
Relation between $E_A$ and $E_B$ cannot be decided based on given information.

Validate

Solution:

Since cars A and B are at same height above the starting point.

∴h=1/2a_Asinθ_At^2=1/2a_Bsinθ_Bt^2

a_A/a_B={sinθ_B}/{sinθ_A}

Given,

sinθ_A > sinθ_B

∴a_A/a_B < 1

∴a_A < a_B

.....(1)
Along the plane,

v_A=a_A×t

v_B=a_B×t

.....[Using (1)]

∴v_A/v_B=a_A/a_B < 1

........[Using (i)]

∴v_A < v_B

T⋅E_A=mgh+1/2mv^2_A

T⋅E_B=mgh+1/2mv^2_B

At a given instant, height is same so potential energywill be same. But due to large speed of B, kinetic energy of B will be more.

∴T⋅E_B > T⋅E_A

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