Centre of Mass & Its Calculation questions with solutions

Showing 1–10 of 47 questions

• NumericmediumCenter of maas , Momentum and CollisionCentre of Mass & Its Calculation

  A uniform triangular lamina has vertices A(0,0), B(6,0) and C(0,6). A smaller triangular lamina with vertices (0,0), (3,0) and (0,3) is removed. If the centre of mass of the remaining lamina is at x(CM) = y(CM) = N/3, find N.

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• MCQmediumCenter of maas , Momentum and CollisionCentre of Mass & Its Calculation

  A circular plate of diameter 56 cm has a circular portion of diameter 42 cm removed from one edge as shown. The centre of mass of the remaining plate is:

  

  Options

  • Option A

    At the original centre

  • Option B

    9 cm left of the bigger-circle centre

  • Option C

    9 cm right of the bigger-circle centre

  • Option D

    14 cm left of the centre

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• MCQmediumCenter of maas , Momentum and CollisionCentre of Mass & Its Calculation

  A square sheet of side 2a has its two right corners folded to the centre O as shown. Taking O=(0,0), centre of mass of the new system is:

  

  Options

  • Option A

    (-a/8,0)

  • Option B

    (-a/6,0)

  • Option C

    (a/12,0)

  • Option D

    (-a/12,0)

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• NumericmediumCenter of maas , Momentum and CollisionCentre of Mass & Its Calculation

  A man of mass 60 kg stands at one end of a uniform boat of mass 40 kg and length 5 m. The boat floats on still water and horizontal external force is negligible. The man walks to the other end. If the magnitude of displacement of the boat is N m, find N.

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• MCQmediumCenter of maas , Momentum and CollisionCentre of Mass & Its Calculation

  A rectangular lamina occupies 0≤x≤a, 0≤y≤b and has surface mass density σ=σ₀x/(ab). Its centre of mass is:

  

  Options

  • Option A

    (2a/3, 2b/3)

  • Option B

    (2a/3, b/2)

  • Option C

    (a/3, b/2)

  • Option D

    (a/2, b/2)

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• MCQmediumCenter of maas , Momentum and CollisionCentre of Mass & Its Calculation

  A 3 kg mass at $\vec{r}_1$ = (2$\hat{i}+5\hat{j}$)m is connected by a massless rod to a 2 kg mass at $\vec{r}_2$ = (4$\hat{i}+2\hat{j}$)m. The rod length and centre-of-mass coordinates are:

  Options

  • Option A

    √13 m and (14/5, 19/5)

  • Option B

    √10 m and (16/5, 17/5)

  • Option C

    5 m and (14/5, 19/5)

  • Option D

    √13 m and (3, 3)

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• MCQeasyCenter of maas , Momentum and CollisionCentre of Mass & Its Calculation

  A thick uniform wire is bent into the shape of the letter U as shown. A is the midpoint of the line joining the midpoints of the two parallel sides. Which labelled point gives the centre of mass of the wire?

  

  Options

  • Option A

    D

  • Option B

    A

  • Option C

    B

  • Option D

    C

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• MCQmediumCenter of maas , Momentum and CollisionCentre of Mass & Its Calculation

  A thin disc of radius R, centred at the origin, has surface mass density σ(x, y) = σ₀(1 + x/R). Its centre of mass lies at:

  Options

  • Option A

    x(CM) = 0

  • Option B

    x(CM) = R/2

  • Option C

    x(CM) = R/4

  • Option D

    x(CM) = R/3

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• MCQmediumCenter of maas , Momentum and CollisionCentre of Mass & Its Calculation

  For a rod of length 3 m with linear density λ = 2 + x, the position of centre of gravity is:

  Options

  • Option A

    7/2 m

  • Option B

    12/7 m

  • Option C

    10/7 m

  • Option D

    9/7 m

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• MCQeasyCenter of maas , Momentum and CollisionCentre of Mass & Its Calculation

  Three identical square plates have one, two and three corners removed as shown. Rank their centres of mass by x-coordinate from smallest to largest.

  

  

  Options

  • Option A

    3, 1, 2

  • Option B

    1, 3, 2

  • Option C

    3, 2, 1

  • Option D

    1 and 3 tie, then 2

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