A uniform rod AB of mass m and length l is suspended by two massless and inextensible strings AC and BD whose ends C and D are fixed as shown. Find the tension in the string BD immediately after the string at A is cut.

A uniform rod AB of mass m and length l is suspended by two massless a

1.	A uniform rod AB of mass m and length l is suspended by two massless and inextensible strings AC and BD whose ends C and D are fixed as shown. Find the tension in the string BD immediately after the string at A is cut.
Answer» Solution :`T cos 37^@=ma_(x)` `:. a_(x)=(4T)/(5m)`…..i `mg-Tsin37^@=ma_(y)` `:. a_(x)=g-(3T)/(5m)`……ii and taking torque about CM of rod, `Tsin37^@ (l/2)=(3l^(2))/12alpha` `:. al=(18T)/(5m)`…..iii Now, since the sting `BD` neither slacks nor breaks, therefore the acceleration of end `B` ALONG the a string must be ZERO. `i.e. a_(y)cos37^@+(al)/2cos53^@-a_(y)cos53^@=0` From eqn i, ii and iii `(4T)/(5m).4/5+(18T)/(5mxx2).3/5-(g-(3T)/(5m))3/5=0` `(52T)/(25m)(3G)/5` `:. T(15mg)/52`