Question

Bodies A and B are rolling without slipping on a rough inclined plane. Match the following: $\begin{array}{cc}\text{Column I}& \text{Column II}\\ \text{A) Velocity of A and B after travelling}& \text{p) different if A and B have same size but}\\ \text{the same distance will be}& \text{different shapes and mass}\\ \text{B) Time taken by A and B to reach the}& \text{q) different if A and B have same size and}\\ \text{bottom of the plane from the same height}& \text{same mass but different shapes}\\ \text{will be}& \\ \text{C) Acceleration of centre of mass A and B}& \text{r) same if A and B have same shapes and}\\ \text{will be}& \text{same size but made up of different materials}\\ \text{D) During rolling motion frictional force}& \text{s) same if A and B have same size but}\\ \text{experienced by A and B will be}& \text{different shapes and mass}\end{array}$

• A. A – p,q,r B – q,r,s C – p,q,r D – s
• B. A – p,q,r B – p,q,r C – p,q D – p,q
• C. A – p,q,r B – q,r,s C – p,q D – p,q
• D. A – p,q,r B – p,q,r C – p,q,r D – p,q

Answer 1

The correct option is D A – p,q,r B – p,q,r C – p,q,r D – p,q

$A)v=\sqrt{\frac{2gh}{1+\frac{k^2}{r^2}}}$ , Hence $v$ depends on the shape and size.

$B)t=\sqrt{\frac{2h(1+\frac{k^2}{r^2})}{gsi{n}^2\theta }}$, Hence $t$ depends on the shape and size.

$C)a=\frac{gsin\theta }{(1+\frac{k^2}{r^2})}$, Hence $a$ depends on the shape and size.

$D)f=\frac{mgsin\theta }{1+\frac{r^2}{k^2}}$, Hence $f$ depends on shape, size and mass.