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PhysicsSingle correct+3 / -1Question 44 of 60

IIT-JEE 2009 · Paper 1, Physics question 44

Look at the drawing given in the figure which has been drawn with ink of uniform line-thickness. The mass of ink used to draw each of the two inner circles, and each of the two line segments is mm. The mass of the ink used to draw the outer circle is 6m6m. The coordinates of the centres of the different parts are: outer circle (0,0)(0,0), left inner circle (−a,a)(-a,a), right inner circle (a,a)(a,a), vertical line (0,0)(0,0) and horizontal line (0,−a)(0,-a). The yy-coordinate of the centre of mass of the ink in this drawing is

A face drawn in ink: a large outer circle centred at the origin, two small circles (eyes) centred at (−a, a) and (a, a), a short vertical line through the origin (nose) and a short horizontal line centred at (0, −a) (mouth); x and y axes are dashed.
Choose one option
Answer and worked solution

Official answer: A

Centre of mass.
ycm=m(a)+m(a)+m(0)+m(−a)+6m(0)m+m+m+m+6m=ma10m=a10.y_\text{cm}=\frac{m(a)+m(a)+m(0)+m(-a)+6m(0)}{m+m+m+m+6m}=\frac{ma}{10m}=\frac a{10}.

(A)

Topics:Centre of mass
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