A triangular loop ABC of string is passed over two small frictionless pulleys A and B. `AB = 2l and BC = AC = eta l`. Two masses m and M are attached to the mid-point O of AB and C respectively and `m` is released. Find the condition that m and M may cross each other.

L and M are the mid points of AB and BC respectively of DeltaABC , right angled at B . 4LC^(2)=

A B C D is a parallelogram. L\ a n d\ M are points on A B\ a n d\ D C respectively and A L=C M . Prove that L M\ a n d\ B D bisect each other.

In DeltaABC , if L and M are the points on AB and AC, respectively such that LM || BC . Prove that ar (DeltaLOB) = ar (DeltaMOC) .

Two blocks each of mass m are connected over two light and frictionless pulleys and a fixed wedge by a light string as shown in figure. The tension in the string is :

ABCD is a parallelogram. L and M are respectively mid points of sides AB and DC. Prove that LD and MB trisects diagonals AC.

Two blocks of masses m and 2m are connected by a light string passing over a frictionless pulley. As shown in the figure, the mass m is placed on a smooth inclined plane of inclination 30° and 2m hangs vertically. If the system is released, the blocks move with an acceleration equal to :

A thin uniformed rod of mass m and length L is hinged at one end and from other end a light string is attached. The string is wound over a frictionless pullely (having mass 2m ) and a block of mass 2m is connected to string on other side of pulley as shown. the system is released from rest when the rod id making an angle of 37^(@) with horizontal. Based on above information answer the following question : Just after releases of the system from rest acceleration of block is

A triangular field ABC, right angled at A has length AC=33m and AB=180m . The length of the side BC is