A drinking straw of length 2 3 a and mass 2 m is placed on a square table of side ' a ' parallel to one of its sides such that one third of its length extends beyond the table. An insect o

Question

A drinking straw of length 2 3 a ​ and mass 2 m is placed on a square table of side ' a ' parallel to one of its sides such that one third of its length extends beyond the table. An insect of mass 2 m ​ lands on the inner end of the straw (i.e., the end which lies on the table) and walks along the straw until it reaches the outer end. It does not topple even when another insect lands on top of the first one. If the largest mass of the second insect that can have without toppling the straw is M , then find m M ​ . Neglect friction.

TestHub · Accepted Answer

Let x be the displacement of straw when the first insect reaches the opposite end. Hence displacement of insect would be ( 2 3 ​ a − x ) . For center of mass to remain stationary we have ____ 2 m ( x ) = 2 m ​ ( 2 3 ​ a − x ) or x = 0.3 a Therefore, the situation is as follows Let M be the mass of second insect. For the straw not to topple the centre of mass (of straw + two insects) should lie inside the table or ​ 2 m ( 0.55 a ) = ( M + 2 m ​ ) ( 0.2 a ) ​ M = 5 m ​

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