Question

68. A man of mass 80 kg carrying a load
of 20 kg walks up a stair case in 20s. If the
number of steps is 40 and width and height
of each step are 20 cm and 15 cm respec
tively. The efficiency of the man is
1) 20%
2) 25%
3) 40%
4) 50%​

Answer 1

The efficiency of the man is 20%.

(1) is correct option.

Explanation:

Given that,

Mass of man M= 80 kg

Load m= 20 kg

Time = 20 sec

Number of steps = 40

Width = 20 cm

Height = 15 cm

We need to calculate the input work done by the man

Using formula of work done

$W_{in}=(m+M)gh$

Put the value into the formula

$W_{in}=(80+20)gh$

$W_{in}=100gh$

We need to calculate the output work done by the man

Using formula of work done

$W_{out}=mgh$

Put the value into the formula

$W_{out}=20gh$

We need to calculate the efficiency of the man

Using formula of efficiency

$\eta=\dfrac{W_{out}}{W_{in}}$

Put the value into the formula

$\eta=\dfrac{20gh}{100gh}$

$\eta=0.2\times100$

$\eta=20%$

Hence, The efficiency of the man is 20%.

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Topic : efficiency

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