question_answer

Two bodies having masses \[{{m}_{1}}=40\,g\] and \[{{m}_{2}}=60\,g\] are attached to the ends of a string of negligible mass and suspended from massless pulley. The acceleration of the bodies is:

A)  \[1\,m/{{s}^{2}}\]         

B)  \[2\,\,m/{{s}^{2}}\]

C)  \[0.4\,\,m/{{s}^{2}}\]       

D)  \[4\,\,m/{{s}^{2}}\]

Correct Answer: B

Solution :

 Let a be acceleration in the masses and T be the tension in the string. The equations of motion are \[{{m}_{2}}=g-T={{m}_{2}}\,a\] ?. (i) \[T-{{m}_{1}}\,g\,={{m}_{1}}\,a\] ... (ii) From Eqs. (i) and (ii), we get \[a=\frac{{{m}_{2}}-{{m}_{1}}}{{{m}_{1}}+{{m}_{2}}}g\] Given, \[{{m}_{2}}=60g,\,{{m}_{1}}=40\,g,\,g=10\,m/{{s}^{2}}\] \[\therefore \] \[a=\frac{60-40}{(60+40)}\times 10=2\,m/{{s}^{2}}\].