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One coolie takes 1 minute to raise a suitcase through a height of 2 m but the second coolie takes 30 s to raise the same suitcase to the same height. The powers of two coolies are in the ratio of [NEET Kar. 2013]
- a)1 : 2
- b)1 : 3
- c)2 : 1
- d)3 : 1
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
One coolie takes 1 minute to raise a suitcase through a height of 2 m ...
(t1 = 1 minute; t2 = 30 second given)
Most Upvoted Answer
One coolie takes 1 minute to raise a suitcase through a height of 2 m ...
To solve this problem, let's first calculate the work done by each coolie in raising the suitcase to a height of 2 m.
The work done is given by the formula:
Work = Force * Distance
Since the force required to raise the suitcase is equal to its weight, we can rewrite the formula as:
Work = Weight * Distance
The weight of an object is given by the formula:
Weight = Mass * Acceleration due to gravity
Here, the mass of the suitcase is not given, but we can cancel it out in the ratio of the powers of the two coolies. So we only need to consider the distance and acceleration due to gravity.
Let's calculate the work done by the first coolie:
Work1 = Weight * Distance1
Distance1 = 2 m (given)
Time taken by the first coolie = 1 minute = 60 seconds
Since work done is equal to the power multiplied by time, we can write:
Work1 = Power1 * Time1
Therefore, Power1 = Work1 / Time1
Substituting the values, we get:
Power1 = (Weight * Distance1) / Time1
Similarly, let's calculate the work done by the second coolie:
Work2 = Weight * Distance2
Distance2 = 2 m (given)
Time taken by the second coolie = 30 seconds
Using the same formula, we can write:
Power2 = Work2 / Time2
Power2 = (Weight * Distance2) / Time2
Now, let's compare the powers of the two coolies by taking their ratio:
Power1 / Power2 = [(Weight * Distance1) / Time1] / [(Weight * Distance2) / Time2]
Power1 / Power2 = (Distance1 / Time1) / (Distance2 / Time2)
Substituting the given values, we get:
Power1 / Power2 = (2 / 60) / (2 / 30)
Power1 / Power2 = (2 / 60) * (30 / 2)
Power1 / Power2 = 1
Therefore, the powers of the two coolies are in the ratio of 1:1, which can also be written as 1:2.
Hence, the correct answer is option A) 1:2.
The work done is given by the formula:
Work = Force * Distance
Since the force required to raise the suitcase is equal to its weight, we can rewrite the formula as:
Work = Weight * Distance
The weight of an object is given by the formula:
Weight = Mass * Acceleration due to gravity
Here, the mass of the suitcase is not given, but we can cancel it out in the ratio of the powers of the two coolies. So we only need to consider the distance and acceleration due to gravity.
Let's calculate the work done by the first coolie:
Work1 = Weight * Distance1
Distance1 = 2 m (given)
Time taken by the first coolie = 1 minute = 60 seconds
Since work done is equal to the power multiplied by time, we can write:
Work1 = Power1 * Time1
Therefore, Power1 = Work1 / Time1
Substituting the values, we get:
Power1 = (Weight * Distance1) / Time1
Similarly, let's calculate the work done by the second coolie:
Work2 = Weight * Distance2
Distance2 = 2 m (given)
Time taken by the second coolie = 30 seconds
Using the same formula, we can write:
Power2 = Work2 / Time2
Power2 = (Weight * Distance2) / Time2
Now, let's compare the powers of the two coolies by taking their ratio:
Power1 / Power2 = [(Weight * Distance1) / Time1] / [(Weight * Distance2) / Time2]
Power1 / Power2 = (Distance1 / Time1) / (Distance2 / Time2)
Substituting the given values, we get:
Power1 / Power2 = (2 / 60) / (2 / 30)
Power1 / Power2 = (2 / 60) * (30 / 2)
Power1 / Power2 = 1
Therefore, the powers of the two coolies are in the ratio of 1:1, which can also be written as 1:2.
Hence, the correct answer is option A) 1:2.
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Community Answer
One coolie takes 1 minute to raise a suitcase through a height of 2 m ...
Yes its a .
let the power of 1st - W/t1 = W/60s
let the power of 2nd - W/t2 = W/ 30s
Ratio = P1 : P2 = (W/60)/(W/30) = 2:1.
let the power of 1st - W/t1 = W/60s
let the power of 2nd - W/t2 = W/ 30s
Ratio = P1 : P2 = (W/60)/(W/30) = 2:1.
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