Q. 31

# Consider the situation shown in figure (5-E14). Both the pulleys and the string are light and all the surfaces are frictionless. (a) Find the acceleration of the mass M. (b) Find the tension in the string. (c) Calculate the force exerted by the clamp on the pulley A in the figure.

Answer :

Let the acceleration of mass *M* be *a*.

So, the acceleration of mass 2*M* will be

(a)

*⇒* *Ma =* *2 T*

*T + Ma − Mg*= 0⇒ Ma2+Ma=Mg

⇒ 3Ma=2Mg ⇒ a=

(b) Tension,

(c) Let *T*' = resultant of tensions

∴ T’=√T^{2}+T^{2}=√2 T

∴ T’=√2T =√ Again, tanθ= =1 **⇒****θ****=45****°**

**So, the force exerted by the clamp on the pulley is √(2mg/3) at an angle of 45° with the horizontal.**

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PREVIOUSCalculate the tension in the string shown in figure (5-E13). The pulley and the string are light and all surfaces are frictionless. Take g = 10 m/s2.NEXTFind the acceleration of the block of mass M in the situation shown in figure (5-E15). Ail the surfaces are frictionless and the pulleys and the string are light.

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