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Let be the volume bounded below by the cone and above by the sphere, lying on the positive side of y–axis, also given that the density of the solid will be . Then consider the following statements :
P : The centre of gravity of the solid will be given by
Q : The moment of inertia of the solid about z–axis is
Consider the following statements about the centre of gravity of the region bounded above by the parabola and below by the x–axis having density .
P : The centre of gravity of the given region will lie on the y–axis.
Q : The x-coordinate of the centre of gravity is equal to .
Then which of the above statement is true?
The centre of mass for the thin plate bounded by the curves and , with density function is :
The centre of mass of a thin wire modelled with a semi-circle of radius with constant density will be :
The centre of mass of the solid lying inside the sphere & outside the sphere with will be :
The coordinates of centre of gravity of the area of the region bounded by the curve and will be given by :
Consider the centre of mass of the tetrahedron in the first octant, bounded by the plane . If the density at a point is equal to the sum of the point coordinates then the x–coordinate of the considered centre of mass would be :
The moment of inertia of a right circular cone whose altitude is and its radius is about its axis will be given by :
The centroid of the area bounded by the parabolas and will be :
The ordered pair stating the moment of inertia with respect to each coordinate axis of the area between the curve from to & the x–axis will be :