State and prove theorem of parallel axis.

State and prove theorem of perpendicular axes.

(a) Prove the theorem of perpendicular axes. (Hint : Square of the distance of a point (x, y) in the x-y plane from an axis through the origin perpendicular to the plane is x^(2)+y^(2) ). (b) Prove the theorem of parallel axes. (Hint : If the centre of mass is chosen to be the origin Sigmam_(1)(r_(i)=0) .

Write carnot theorem.

State and prove Pascal's law.

The tangent at a point P of a curve meets the y-axis at A, and the line parallel to y-axis through P meets the x-axis at B. If area of DeltaOAB is constant (O being the origin), Then the curve is

Prove that the force acting on one plate due to the other in a parallel plate capacitor is F =(1)/(2) (CV^(2))/(d) .

State the merits and demerits of a parallel combination of resistors.

If a transversal intersects two lines such that the bisectors of a pair of corresponding angles are parallel, then prove that the two lines are parallel.

Prove that two triangles on the same base and between the same parallels are equal in area.