Calculate the maximum acceleration of a moving car so that a body lying on the floor of the car remains stationary. The coefficient of static friction between the body and the floor is 0.15

$$\left(g=10 \mathrm{~m} \mathrm{~s}^{-2}\right)$$.

A bullet from a gun is fired on a rectangular wooden block with velocity $$u$$. When bullet travels $$24 \mathrm{~cm}$$ through the block along its length horizontally, velocity of bullet becomes $$\frac{u}{3}$$. Then it further penetrates into the block in the same direction before coming to rest exactly at the other end of the block. The total length of the block is :

If $$\overrightarrow F = 2\widehat i + \widehat j - \widehat k$$ and $$\overrightarrow r = 3\widehat i + 2\widehat j - 2\widehat k$$, then the scalar and vector products of $$\overrightarrow F $$ and $$\overrightarrow r $$ have the magnitudes respectively as

In the diagram shown, the normal reaction force between 2 kg and 1 kg is (Consider the surface, to be smooth) :

(Given g = 10 ms^$$-$$2)