A uniform bar AB of length `6a` has been placed on a horizontal smooth table of width 5 a as shown in the figure. Length 2a of the bar is overhanging. Mass of the bar is 4m. An insect of mass m is sitting at the end A of the bar. The insect walks along the length of the bar to reach its other end B.

(a) Will the bar topple when the insect reaches end B of the bar ?
(b) After the insect reaches at B, another insect of mass M lands on the end A of the bar. Find the largest value of M which will not topple the bar.

Does the length of each bar depend on the lengths of other bars in the graphs?

A uniform bar of length 12 L and mass 48 m is supported horizontally on two smooth tables as shown in the figure. A small moth (an insect) of mass 8m is sitting on end A of the rod and a spider (an insect) of mass 16 m is sitting on the other end B . Both the insects start moving towards each other along the rod with the moth moving at speed 2v and the spider at half of this speed. They meet at a point P on the rod and the spider eats the moth. Also, let v = L//T , where T is a constant having value 4 sec . The point P is at

A uniform bar of length 12 L and mass 48 m is supported horizontally on two smooth tables as shown in the figure. A small moth (an insect) of mass 8m is sitting on end A of the rod and a spider (an insect) of mass 16 m is sitting on the other end B . Both the insects start moving towards each other along the rod with moth moving at speed 2v and the spider at half of this speed. They meet at a point P on the rod and the spider eats the moth. After this the spider moves with a velocity v//2 relative to the rod towards the end A . The spider takes negligible time in eating the insect. Also, let v = L//T , where T is a constant having value 4 sec . The speed of the bar after the spider eats up the moth and moves towards A is

A uniform bar of length 12 L and mass 48 m is supported horizontally on two smooth tables as shown in the figure. A small moth (an insect) of mass 8m is sitting on end A of the rod and a spider (an insect) of mass 16 m is sitting on the other end B . Both the insects start moving towards each other along the rod with moth moving at speed 2v and the spider at half of this speed. They meet at a point P on the rod and the spider eats the moth. After this the spider moves with a velocity v//2 relative to the rod towards the end A . The spider takes negligible time in eating the insect. Also, let v = L//T , where T is a constant having value 4 sec .The speed of the bar after the spider eats up the moth and moves towards A is

A uniform bar of length 12L and mass 48m is supported horizontally on two fixed smooth tables as shown in figure. A small moth (an insect) of mass 8m is sitting on end A of the rod and a spider (an insect) of mass 16m is sitting on the other end B. Both the insects moving towards each other along the rod with moth moving at speed 2v and the spider at half this speed (absolute). They meet at a point P on the rod and the spider eats the moth. After this the spider moves with a velocity v/2 relative to the rod towards the end A. The spider takes negligible time in eating on the other insect. Also, let v=L/T where T is a constant having value 4s . After starting from end B of the rod the spider reaches the end A at a time

A uniform bar of length 6a and mass 8 m lies on a smooth horizontal table. Two point-masses m and 2m moving in the same horizontal plane with speeds 2v and v respectively strike the bar as shown in Fig, and stick to the bar after collision.

A bar of mass m and length l is hanging from point A as shown in the figure . If the Young's modulus of elasticity of the bar is Y and area of cross - section of the wire is A, then the increase in its length due to its own weight will be

A bar of mass m and length l is hanging from point A as shown in the figure . If the Young's modulus of elasticity of the bar is Y and area of cross - section of the wire is A, then the increase in its length due to its own weight will be

Find the acceleration of the prism of mass M and that of the bar of mass m shown in figure.