A block rests on a rough inclined plane `making an angle of $${30^ \circ }$$ with the horizontal. The coefficient of static friction between the block and the plane is $$0.8.$$ If the frictionless force on the block is $$10$$ $$N,$$ the mass of the block (in $$kg$$) is $$\left( {take\,\,\,g\, = \,10\,\,m/{s^2}} \right)$$

A spring balance is attached to the ceiling of a lift. A man hangs his bag on the spring and the spring reads $$49$$ $$N,$$ when the lift is stationary. If the lift moves downward with an acceleration of $$5 m/{s^2}$$, the reading of the spring balance will be

A light spring balance hangs from the hook of the other light spring balance and a block of mass $$M$$ $$kg$$ hangs from the former one. Then the true statement about the scale reading is

A marble block of mass $$2$$ $$kg$$ lying on ice when given a velocity of $$6$$ $$m/s$$ is stopped by friction in $$10$$ $$s.$$ Then the coefficient of friction is