1.

A block of mass m_(1) = 1 kg and anothermass m_(2) = 2 kg are placed together ( see figure) on an inclined plane withangle of inclinationtheta . Various values of theta are given in List I . The coefficient of friction between the block m_(1) and the plane is always zero. The coefficient of static and dynamic friction between the block m_(2) and the plane are equal to mu = 0.3 . In List II expressions for the friction on the block m_(2) are given .Match the correct expression of the friction in List II with the angles given in List I , and choose the option . The acceleration due to gravity is denoted by g . [Useful information : tan ( 5. 5^(@)) = 0.1, tan (11. 5^(@)) = 0.2 , tan (16.5 ^(@)) = 0.3] {:(,"List" I ,, "List" II), (P. , theta = 5^(@) , 1., m_(2)g sin theta ) , (Q. , theta= 10^(@) , 2., (m_(1) + m_(2))g sin theta), (R., theta = 15^(@) , 3., mu m_(2)g cos theta), (S., theta = 20^(@) , 4., mu (m_(1) + m_(2))g cos theta):}

Answer»

P-1 , Q-1 , R-1 , S-3
P-2 , Q-2 ,R-2 , S-3
P-2 , Q-2 , R-2 , S- 4
P-2 , Q-2 , R-3 , S-3

Solution :Condition for not sliding
`f_("max") gt (m_(1) + m_(2) )gsin theta `
`mu_(N) gt (m_(1) + m_(2)) g sin theta `
`0.3 m_(2) g cos theta ge (1 +2) 10 sin theta `
`0.3 xx 2 xx 10 cos theta ge (1 +2) 10 sin theta `
`6 ge 30 TAN theta `
`(1)/(5) ge tan theta "" implies 0.2 ge tan theta `
Now it is CLEAR in case (P) (Q) it will not slip, friction is `(m_(1) + m_(2)) g sin theta `.

`implies f = (m_(1) + m_(2)) g sin theta `
In the case (R) (S) if they MUST slip so friction should be KINETIC i.e.,
`mu m_(2) g cos theta `


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