Question

Which of the following statements are incorrect?
(i) If there were no friction, work need to be done to move a body up an inclined plane is zero.
(ii) If there were no friction, moving vehicles could not be stopped even by locking the brakes
(iii)As the angle of inclination is increased, the normal reaction on the body placed on it increases
(iv) A duster weighing $0.5kg$ is pressed against a vertical board with a force of $11N$ . If the coefficient of friction is $0.5$ , the work done in rubbing it upward through a distance of $10cm$ is $0.55J$

• A. (i) and (ii)
• B. (i), (ii), (iv)
• C. (ii) and (iii)
• D. All of these

Answer 1

Answer: (C)

The explanations are given below
(i) If a body is moved up an inclined plane, then the work done against friction force is zero as there is no friction. But a work has to be done against the gravity So, this statement is incorrect
(ii) If there were no friction, moving vehicles could not be stopped by locking the brakes Vehicles are stopped by air friction only So, this statement is correct
(iii) In this situation the normal reaction is given by

$R=mgcos\alpha \dots \left(i\right)$
If $\alpha$ increases then the value of $cos\alpha$ decreases and hence, normal reaction $R$ also decreases
So, this statement is incorrect
(iv) When the duster is rubbing upward then an external force is applied and its value is

$F^{\prime }=0.5g+\mu R$
$\therefore F^{\prime }=0.5g+5.0\times 11$
or $F^{\prime }=\left(0.5\times 10+5.5\right)N$ [Here $R=11N$]
or $F^{\prime }=10.5N$
Hence, work done in rubbing the duster through a distance of $10cm$
$W=F^{\prime }\times d$
$\Rightarrow W=10.5\times \frac{10}{100}J$
or $W=1.05J$
Hence, none of the options is correct