GATE Mechanical Engineering (ME) 2020 Shift 1 Solved Paper

Question : 27 of 65

Marks: +1, -0

A balanced rigid disc mounted on a rigid rotor has four identical point masses, each of 10 grams, attached to four points on the

100 {mm}

radius circle shown in the figure.

The rotor is driven by a motor at uniform angular speed of

10 {rad} {/} {s}

. If one of the masses gets detached then the magnitude of the resultant unbalance force on the rotor is _____________

{N}

(round off to 2 decimal places).

Solution:

If mass A is removed, then system becomes unbalanced.

F resultant

=

Net unbalanced force

=√{(Σ F_{x})^{2}+(Σ F_{y})^{2}}

Σ {F}_{ {x}}=mr ω^{2}(\cos 90^{∘}+\cos 180^{∘}+\cos 270^{∘})

=m r ω^{2}(0-1+0)

Σ f_{x}=-0.1

Similarly,

Σ {F}_{ {y}}=mr ω^{2}(\sin 90^{∘}+\sin 180^{∘}+\sin 270^{∘})

Σ f_{y}=0

{F}_{ {r}}=√{(∑ {F}_{ {x}})^{2}+(∑ {F}_{ {y}})^{2}}

{Fr}=0.1 {N}=

Net unbalanced force.

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