A box is lying on the floor of a moving train and the coefficient of friction between the floor and the box is 0.24. Find the maximum acceleration of the train for which the box will lie stationary on the floor. Given that `g=9.8 ms^(-2)`.

A block of mass 15 kg is placed on a long trolley. The coefficient of friction between the block and the trolley is 0.18. The trolley accelerate from rest with 0.5 ms^-2 for 20 s and then moves with unifrom velocity. Discuss the motion of the block as viewd by an observer with the trolley.

The radius of curvature of a railway track at a place where the train is moving at a speed of 72 km h^-1 is 625 m.The distance between the rails is 1.5 m.Find the angle and the elevation of the outer rail so that there may be no side pressure on the rails. (g=9.8 m s^(-2)) .

The rear side of a truck is open and a box of 40 kg mass is placed 5 m away from the open end as shown. The coefficient of friction between the box and the surface below its is 0.15. On a straight road, the truck starts from rest and accelerates with 2 ms^-2 . At what distance from the starting point does the box fall off the truck ?/ (Ignore the size of the box).

The rear side of a truck is open and a box of 40 kg mass is placed 5 m away from the open end as shown in Fig. 5.22. The coeffcient of friction between the box and the surface below it is 0.15. On a straight road, the truck starts from rest and accelerates with 2 m s^-2 . At what distance from the starting point does the box fall off the truck? (Ignore the size of the box).

What is the acceleration of the block and trolley system shown in the figure, if the coefficient of kinetic friction between the trolley and the surface is 0.04?/ What is the tension in the string? (Take g = 10 ms^-2 ) Neglect the mass of the string.

As shown in the given figure. the two sides of a step ladder BA and CA are 1.6 m long and hinged at A.A rope DE, 0.5 m is tied half way up. A weight 40 kg is suspended from a point F, 1,2 m from B along the ladder BA. Assuming the floor to be frictionless and neglecting the weight of the ladder, find the tension in te rope and forces exerted by the floor on the ladder. (Take g = 9.8 ms^-2 ) (Hint: consider the equilibrium of each side of the ladder separately).

A cyclist goes round a circular path of radius 20.0 m with a speed of 14 m s^-1 .Find the angle through which his cycle makes with vertical. (g=9.8 ms ^-2) .

Give the magnitude and direction of the net force acting on a stone of mass 0.1kg:- lying on the floor of a train which is accelerating with 1 m s^-2 , the stone being at rest relative to the train.Neglect air resistance throughout.