In the figure shown, all pulleys are massless and the strings are light. What is the acceleration of the block m of mass 10kg? (All surfaces are smooth and take g=10m/s2.)
A
4.5m/s2 down the plane
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B
4.5m/s2 up the plane
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C
5m/s2 down the plane
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D
5m/s2 up the plane
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Solution
The correct option is A4.5m/s2 down the plane The given system can be framed as shown
FBDs of the pulleys and the blocks are as shown. Let T be the tension in the string connected to pulley P7.
Let a be the acceleration of block m.
For P7:80−2T=ma7⇒T=40N as m=0 For the block: The acceleration of the block a is given as 10gsin30°−408=10a 10×10×12−5=10a a=4.5m/s2 down the plane