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CBSE Class 12-science Answered

Two rings each of mass M-100 gm are constrained to move along a fixed horizontal rod An ideal string is connected with rings and block of mass M, = 200 gm is connected to the mid point of string At a certain moment the mass m is moving downward with velocity √3 m/s. Find the speed of ring of M at the moment: M 2m 2m M 30° 30° Molvo = √3 m/s
Asked by 11soumya09 | 29 Sep, 2023, 07:35: PM
answered-by-expert Expert Answer
 
Let l be the semi-length between rings and h be the distance between mass and rod as shown in figure.
 
when the mass is always at centre of string, then we have
 
begin mathsize 14px style l squared space plus space h squared space equals space c o n s tan t end style ...............................(1)
if we differentiate above eqn.(1) , then we get
 
begin mathsize 14px style 2 space l space fraction numerator d l over denominator d t end fraction plus space 2 space h space fraction numerator d h over denominator d t end fraction space equals space 0 end style
 
where dl/dt is speed of ring and dh/dt is speed of mass .
 
Then from above expression, we get
 
begin mathsize 14px style fraction numerator d l over denominator d t end fraction equals space minus h over l cross times fraction numerator d h over denominator d t end fraction end style
Answered by Thiyagarajan K | 29 Sep, 2023, 08:32: PM
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