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Physics-

General

Easy

Question

A plank is held at an angle $alpha$ to the horizontal on two fixed supports $A$ and $B$ . The plank can slide against the supports (without friction) because of the weight $M g sin invisible function application alpha$ . Acceleration and direction in which a man of mass $m$ should move so that the plank does not move are
<img src="https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/965297/1/1211140/Picture59.png" alt=""

$g \sin α (1 + \frac{m}{M})$ down the incline
$g \sin α (1 + \frac{M}{m})$ down the incline
$g \sin α (1 + \frac{m}{M})$ up the incline
$g \sin α (1 + \frac{M}{m})$ up the incline

hint Hint:

f=mgsinalpha

The correct answer is: $g sin invisible function application alpha open parentheses 1 plus fraction numerator M over denominator m end fraction close parentheses$ down the incline

Free-body diagram of man and plank is given below figure

For plank to be at rest, applying Newton’s second law to plank along the incline
$M g sin invisible function application alpha equals f$ (i)
And applying Newton’s second law to man along the incline
$m g sin invisible function application alpha plus f equals m a$ (ii)
$rightwards double arrow a equals g sin invisible function application alpha open parentheses 1 plus fraction numerator M over denominator m end fraction close parentheses$ down the incline

Related Questions to study

A wooden block of mass $M$ resting on a rough horizontal floor is pulled with a force $F$ at an angle $ϕ$ with the horizontal. If $mu$ is the coefficient of kinetic friction between the block and the surface, then the acceleration of the block is

A wooden block of mass $M$ resting on a rough horizontal floor is pulled with a force $F$ at an angle $ϕ$ with the horizontal. If $mu$ is the coefficient of kinetic friction between the block and the surface, then the acceleration of the block is

Physics-General

Read the story and answer the questions
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