JEE Main · 2024 · 08 Apr 2024 · Shift 1 · Conservation of Momentum

A uniform thin metal plate of mass 10 kg with dimensions is shown. The ratio of

x

and

y

coordinates of center of mass of plate in

\frac{n}{9}

.The value of n is ____.

Answer: 15

Solution

Treat the plate as the full rectangle (mass

m_{3} = 12

units for area 6) built from the notched plate (given

m_{1} = 10

kg, area 5) plus the missing square (mass

m_{2} = 2

, area 1) at its centre

(1.5, 1.5)

.
Using

m_{1} x_{1} + m_{2} x_{2} = m_{3} x_{3}

10 x_{1} + 2 (1.5) = 12 (1.5) \Rightarrow x_{1} = 1.5 cm

.
Using

m_{1} y_{1} + m_{2} y_{2} = m_{3} y_{3}

10 y_{1} + 2 (1.5) = 12 (1) \Rightarrow y_{1} = 0.9 cm

\frac{x _{1}}{y _{1}} = \frac{1.5}{0.9} = \frac{15}{9} = \frac{n}{9} \Rightarrow n = 15

JEE Main · 2024 · 08 Apr 2024 · Shift 1 · Integer answer

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