SSC JE Mechanical Engineering 2014 Set 1 Paper

Question : 101 of 200

Marks: +1, -0

MECHANICAL

The twining moment (T) delivered by a flywheel with respect to its angular displacement is given by the following expression :
T = 14000 + 7000 sin θ
The values of θ for which delivered torque is equal to mean torque for a single cycle are

0°, 180°, 360°
90°, 270°, 360°
90°, 270°, 180°
0°, 270°, 360°

Validate

Solution:

T_\mean=1/{2π}∫↖{2π}↙{0}T.dθ

=1/{2π}∫↖{2π}↙{0}((14000 +7000\sinθ)dθ

=1/{2π}(14000θ-7000\cosθ)^{2π}_0

∵ \cos2π=1

= 14000 N-m
T

_\mean

will be equal to delivered torque
T

_\mean=14000

_\delivered = 14000 + 7000 \sinθ

14000 = 14000 + 7000 sinθ
sinθ = 0
θ = 0°, 180°, 360°

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