Question
A block of mass $$m = 1\,kg$$ is moving with a constant acceleration $$a = 1\,m/{s^2}$$ on a rough horizontal plane. The coefficient of friction between the block and plane is $$\mu = 0.1.$$ The initial velocity of block is zero at $$t = 0.$$ The power delivered by the external agent at a time $$t = 2\,\sec$$ from the beginning is equal to (Take $$g = 10\,m/{s^2}$$ )
A.
$$1\,watt$$
B.
$$2\,watt$$
C.
$$3\,watt$$
D.
$$4\,watt$$
Answer :
$$4\,watt$$
Solution :
$$\eqalign{ & m = 1\,kg,a = 1\,m/{s^2},\mu = 0.1 \cr & f = \mu mg = 0.1 \times 1 \times 10 = 1N \cr & {F_{{\text{ext}}}} = ma + f \cr & {F_{{\text{ext}}}} = 1 + 1 = 2N \cr & v = u + at = 0 + 1 \times 2 = 2\,m/\sec . \cr & \therefore P = {F_{{\text{ext}}}} \cdot v = 2 \times 2 = 4\,watt. \cr} $$
$$\eqalign{ & m = 1\,kg,a = 1\,m/{s^2},\mu = 0.1 \cr & f = \mu mg = 0.1 \times 1 \times 10 = 1N \cr & {F_{{\text{ext}}}} = ma + f \cr & {F_{{\text{ext}}}} = 1 + 1 = 2N \cr & v = u + at = 0 + 1 \times 2 = 2\,m/\sec . \cr & \therefore P = {F_{{\text{ext}}}} \cdot v = 2 \times 2 = 4\,watt. \cr} $$