Question

A plant is held at an angle a to the horizontal (figure) on two fixed supports A and B. The plank can slide against the supports (without friction) because of it's weight Mg. Acceleration and direction in which a man of mass m should move so that the plank does not move –

• A. g sin a $\left[ 1 + \frac { \mathrm { m } } { \mathrm { M } } \right]$ down the incline
• B. g sin a $\left[ 1 + \frac { \mathrm { M } } { \mathrm { m } } \right]$ down the incline
• C. g sin a $\left[ 1 + \frac { \mathrm { m } } { \mathrm { M } } \right]$ up the incline
• D. g sin a $\left[ 1 + \frac { \mathrm { M } } { \mathrm { m } } \right]$ up the incline

Answer 1

Answer: (A)

g sin a $\left[ 1 + \frac { \mathrm { m } } { \mathrm { M } } \right]$ down the incline

Answer 2

F.B.D. of man and plank are

For plank to be at rest, applying Newton's second law of plank along the incline

Mg sin a = f ….. (1)

and applying Newton's second

law of man along the incline

Mg sin a + f = ma …..(2)

a = g sin a $\left[ 1 + \frac { \mathrm { M } } { \mathrm { m } } \right]$ down the incline