Question

Statement I : A work done by the friction is always negative
Statement II : If frictional force acts on a body its kinetic energy may decrease
A) Statement-I is false, Statement-II is true
B) Statement-I is true, Statement-II is true, Statement-II is correct explanation for statement-I
C) Statement-I is true, Statement-II is true, Statement-II is not correct explanation for statement-I
D) Statement-I is false, Statement-II is false

Answer 1

Hint: Approaching process is based on formula
For work done, $=Force\times \text{distance}=Fd\cos \theta$ where $\theta$ is the angle between force and distance travelled So, clearly work done will be Zero when force is perpendicular to the distance travelled, maximum or positive when force acts in the direction of distance travelled and minimum or negative when force acts opposite to the direction of distance travelled.
For friction, $f=\mu N$ where $\mu$ is the coefficient of friction and $N$ is the normal reaction. Coefficient of friction is also of two types that is kinetic and static denoted by ${\mu }_{k}and{\mu }_s$ kinetic friction comes into action when body is in motion state and static friction acts when the body is in motion.

Complete step by step answer:
According to the question given let us first examine the first statement which says that the work done by friction is always negative. Reconsider the above formula, kinetic friction always opposes the motion but static not so, hence, statement second is correct because kinetic friction sometimes acts in the opposite direction of motion which may decrease the kinetic energy .Static friction may or may not be negative which may or may not decrease the kinetic energy for example while walking on the ground static friction acts in the direction of motion which makes us stable to walk and that is also the reason why we want our shoes non slippery and rough.
Basically static friction can also act when a body is in equilibrium and hence displacement is zero and hence work done by static friction is zero.
Coming to the First statement, which is clearly a false statement as discussed in above example.
Therefore the correct option is A

Note: Normal always perpendicular to the surface and passes through the centre of the body.
Frictional force is a self-adjusting force, in case of static friction it will act in such a way just to cancel the effect of the force applied and when it reaches its maximum limit the body starts to move and then kinetic friction comes into play whose maximum value is little smaller than the maximum value of static friction.