A homogeneous plate `PQRST` is as shown in figure. The centre of mass of plate lies at midpoint `A` of segment `QT`. Then the ratio of `(b)/(a)` is `(PQ=PT=b,QR=RS=a)`

Two uniform plates of the same thickness and area but of different materials, one shaped like an isosceles triangle and the other shaped like a rectangle are joined together to form a composite body as shown in the figure. If the centre of mass of the composite body is located at the midpoint of their common side, the ratio between masses of the triangle to that of the rectangle is -

Centre of mass of the system lies inside disc or square plate and why ?

Find the centre of mass of a homogeneous semicircular plate of radius a.

A uniformly thick plate in the shape of an arrow head has dimensions as shown. The centre of mass lies at a point.

A uniform square plate of mass m is supported with its plane vertical as shown in the figure. Assume the centre of mass is on a horizontal the passing through A. If the cable at B breaks then just after that the angular acceleration of the plate is

A uniform square plate of mass m is supported with its plane vertical as shown in the figure. Assume the centre of mass is on a horizontal the passing through A. If the cable at B breaks then just after that the angular acceleration of the plate is

A slab of copper of thickness b is inserted in between the plates of parallel plate capacitor as shown in figure. The separation of the plate is d . If b=d//2 , then the ratio of capacities of the capacitor after and before inserting that slab will be