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Physics-

General

Easy

Question

A block of mass $m subscript 1 end subscript$ lies on the top of fixed wedge as shown in figure [a] and another block of mass $m subscript 2 end subscript$ lies on top of wedge which is free to move as shown in figure [b]. Attime $t equals 0$ , both the blocks are released from rest from a vertical height $h$ above the respective horizontal surface on which the wedge is placed as shown. There is no friction between block and wedge in both the figures. Let $T subscript 1 end subscript$ and $T subscript 2 end subscript$ be the time taken by the blocks, respectively, to just reach the horizontal surface
<img src="https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/965250/1/1211141/Picture61.png" alt=""

$T_{1} > T_{2}$
$T_{1} < T_{2}$
$T_{1} = T_{2}$
Data insufficient

hint Hint:

T2<T1

The correct answer is: $T subscript 1 end subscript greater than T subscript 2 end subscript$

In first case, acceleration of $m subscript 1 end subscript$ will be $a subscript 1 end subscript equals g sin invisible function application theta$ down the inclined plane. In second case,

Acceleration of $m subscript 2 end subscript$ w.r.t. incline is
$a subscript 2 end subscript equals fraction numerator m subscript 2 end subscript g sin invisible function application theta plus m subscript 2 end subscript a cos invisible function application theta over denominator m subscript 2 end subscript end fraction blank rightwards double arrow blank a subscript 2 end subscript equals g sin invisible function application theta plus a cos invisible function application theta$
Since $a subscript 2 end subscript greater than a subscript 1 end subscript$ , so $T subscript 2 end subscript less than T subscript 1 end subscript$

Related Questions to study

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=""

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=""

Physics-General

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

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Physics-General

Read the story and answer the questions
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