Persons A and B are standing on opposite sides of a 3.5 ,m wide water stream which they wish to cros

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6.System of Particles and Rotational Motion

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Persons $A$ and $B$ are standing on the opposite sides of a $3.5 \,m$ wide water stream which they wish to cross. Each one of them has a rigid wooden plank whose mass can be neglected. However, each plank is only slightly longer than $3 \,m$. So, they decide to arrange them together as shown in the figure schematically. With $B$ (mass $17 \,kg$ ) standing, the maximum mass of $A$, who can walk over the plank is close to ............ $kg$

A

$17$

B

$65$

C

$80$

D

$105$

(KVPY-2017)

Solution

(c)

When planks are arranged as given in question, we have following situation.

Let $m=$ maximum mass of $A$.

Then, for safe crossing,

$m g \times 0.5=17 \times g \times 2.5$

$\Rightarrow m=\frac{17 \times 2.5}{0.5}=85 \,kg$

So, a man of mass upto $80 \,kg$ can pass over planks.

Standard 11

Physics

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