Alok is planning a garden in triangular sections in which `DeltaCFD and deltaHFG` to be congruent. F is the midpoint of DGand `DG =16m`.

Two point charges +q and -q are placed at point A and B respectively which are at a distance 2m apart. C is the midpoint between A and B. The work done by external agent in moving a charge Q slowly along the triangular path CED (AC=BC=BD)

A wedge of mass m and triangular cross- section (AB = BC = CA = 2R) is moving with a constant velocity -v hat I towards a sphere of radius R fixed on a smooth horizontal table as shown in figure. The wadge makes an elastic collision with the fixed sphere and returns along the same path without any rotaion. Neglect all friction and suppose that the wedge remains in contact with the sphere for a very shot time. Deltat, during which the sphere exerts a constant force F on the wedge. (a) Find the force F and also the normal force N exerted by the table on the wedge during the time Deltat. (b) Ler h denote the perpendicular distance between the centre of mass of the wedge and the line of action of F. Find the magnitude of the torque due to the normal force N about the centre of the wedge, during the interval Deltat.

A wedge of mass m and triangular cross- section (AB = BC = CA = 2R) is moving with a constant velocity -v hat I towards a sphere of radius R fixed on a smooth horizontal table as shown in figure. The wadge makes an elastic collision with the fixed sphere and returns along the same path without any rotaion. Neglect all friction and suppose that the wedge remains in contact with the sphere for a very shot time. Deltat, during which the sphere exerts a constant force F on the wedge. (a) Find the force F and also the normal force N exerted by the table on the wedge during the time Deltat. (b) Ler h denote the perpendicular distance between the centre of mass of the wedge and the line of action of F. Find the magnitude of the torque due to the normal force N about the centre of the wedge, during the interval Deltat.

Which of the following pairs of triangles are congruent? If they are congruent, write out the pairs of equal angles. A B C : A B=3c m , B C=4c m , C A=2 c m D E F : D E=2 c m , E F=3 c m a n d F D=4 c m P Q R : P Q=17 c m , Q R=15 c m , P R=18 c m D E F : D E=18 c m , E F=17 c m , D F=15 c m .

Which of the following pairs of triangles are congruent? If they are congruent, write out the pairs of equal angles. A B C : A B=3c m ,\ B C=4c m ,\ C A=2\ c m D E F : D E=2\ c m ,\ E F=3\ c m\ a n d\ F D=4\ c m P Q R : P Q=17\ c m ,\ Q R=15\ c m ,\ P R=18\ c m D E F : D E=18\ c m ,\ E F=17\ c m ,\ D F=15\ c m .

The cross section of a prism is a regular hexagon. A narrow beam of light strikes a face of the prism just below the midpoint (M) of the edge AB. The beam is parallel to the top and bottom faces of the prism. Final the minimum value of refractive index of the material of the prism for which the emergent beam will be parallel to the incident beam.

A floral design on a floor is made up of 16 tiles which are triangular, the sides of the triangle being 9c m ,\ 28 c m\ a n d\ 35 c m (See Figure). Find the cost of polishing the tiles at the rate of 50\ p a i s e\ p e r\ c m^2 .

A small cubical block is placed on a triangular block M so that they touch each other along a smooth inclined contact plane as shown in fig. The inclined surface makes an angle theta with the horizontal. A force F is to be appled on the block m in horizontal direction so that the two bodies move without slipping against each other assuming the floor to be smooth also. determine the (a) normal force with which m and M press against each other. (b) magnitude of external force F. Express your answer in terms of m, M, theta ,and g.