A box is lying on the floor of a moving train and coefficient of the friction between the floor and the box 0.15. Find the maximum acceleration of the trainfor which the box will lie stationaryon the floor. Given g= 10m/s

Let the mass of the box be ‘m’. The force of gravity on the box is = mg

So, the maximum static friction is, f = µmg

Now, let ‘a’ be the maximum acceleration of the train. So, the magnitude of the pseudo force acting on the box opposite to the direction of acceleration of the train is = ma

For the box to be in equilibrium,

µmg = ma

=> a = µg = 0.15 × 10

=> a = 1.5 m/s²