Question

In figure, the coefficient of friction between the floor and the block B is 0.1. The coefficient of friction between the blocks B and A is 0.2. The mass of a is m/2 and of B is m. What is the maximum horizontal force F can be applied to the block B so that two blocks move together?

• A. 0.15 mg
• B. 0.05 mg
• C. 0.1 mg
• D. 0.45 mg

Answer 1

Answer: (D)

0.45 mg

Answer 2

Here $m _ { A } = \frac { m } { 2 } , m _ { B } = m$

$\mu _ { A } = 0.2 , \mu _ { B } = 0.1$

Let both the blocks are moving with common acceleration a then

$a = \frac { \mu _ { A } m _ { A } g } { m _ { A } } = \mu _ { A } g = 0.2 g$

And $F - \mu _ { B } \left( m _ { B } + m _ { A } \right) g = \left( m _ { B } + m _ { A } \right) a$ $F = \left( m _ { B } + m _ { A } \right) a + \mu _ { B } \left( m _ { B } + m _ { A } \right) g$ $= \left( m + \frac { m } { 2 } \right) ( 0.2 g ) + ( 0.1 ) \left( m + \frac { m } { 2 } \right) g$ $= \left( \frac { 3 } { 2 } m \right) ( 0.2 g ) + \left( \frac { 3 } { 2 } m \right) ( 0.1 g ) = \frac { 0.9 } { 2 } m g = 0.45 m g$