Q25 of 82 Page 79

Consider the situation shown in figure (5-E9). All the surfaces are frictionless and the string and the pulley are light. Find the magnitude of the acceleration of the two blocks.


Mass of each block is 1 kg, sin θ1=45, sin θ2=35.
The free-body diagrams for both the boxes are shown below:

mgsinθ1 − T = ma ...(i)
T − mgsinθ2 = ma ...(ii)
Adding equations (i) and (ii),we get: mg(sinθ1− sinθ2) = 2ma
 ⇒ 2a = g (sinθ1 − sinθ2)
 ⇒ a= ×12 =


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Figure (5-E8) shows a uniform rod of length 30 cm having a mass of 3.0 kg. The strings shown in the figure are pulled by constant forces of 20 N and 32 N. Find the force exerted by the 20 cm part of the rod on the 10 cm part. All the surfaces are smooth and the strings and the pulleys are light.


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