Two masses 8 kg and 12 kg are connected at the two ends of a light inextensible string that goes over a frictionless pulley. Find the acceleration of the masses and the tension in the string when the masses are released.

Two masses 8 kg and 12 kg are connected at the two ends of a light ine

1.	Two masses 8 kg and 12 kg are connected at the two ends of a light inextensible string that goes over a frictionless pulley. Find the acceleration of the masses and the tension in the string when the masses are released.
Answer» Solution :Let `m_(1)= 8 kgm_(2)= 12 KG` Lettensionin stringbe T Let commonaccelerationof systemisa Accelerationof `m_(1)`is inupwarddirectionaccelerationof `m_(2)`is indownwarddirectionequationof motionof `m_(1)` Bytakingadditionof equation(1) and(2) we getcommonaccelerationof SYSTEM `(m_(2)- m_(1))g= (m_(1) + m_(2))a` `=((12-8)/( 8+12))xx 10` `T = m_(1)g + m_(1)((m_(2)-m_(1))/( m_(1)+ m_(2))) g` `T= ((2m_(1)m_(2))/( m_(1)+m_(2)))g` Substitutingvalue `T=(2xx 8 xx 12)/( 8+ 12)xx 10` `T= (2xx960)/(20)` `:. T = 96 N` Letmass ofnucleusis mandinitialvelocityv= 0 initialmomentum`vec(p )_(1)=- mV =0` Afterdisintergrationit isdividedintotwopartlet mass be `m_(1)`and `m_(2)`and velocitybe `vec( V ) _(1)`and`vec(2)` respectively By lawof conservationof linearmomentum `vec(p )_(1)= vec( p)_(f)` `:.,m_(2)v_(2)= -m_(1) m_(1)` Negativesighshowsthatvelocityof bothfragmentare inmutuallyoppositedirection