A bob of weight 0.1 N hangs from a massless string of length 50 cm. A variable horizontal force which increase from zero is applied to pull the bob until the string makes an angle of 60o with the vertical. The work done is?
0.500 J
0.250 J
0.050 J
0.025 J
Explanation
Video Explanation
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Discussions (15)
The answer is very coreect
work done=FSCOSØ
Convert 50cm to M=0.5
Work done=0.1*0.5*COS60
W=0.05*0.5(Cos60)
W=0.025J
i Hope u understand better
Workdone = force * distance
Workdone =weight *distance
Since the force hasn't make angle 90 it means it has components in the direction of the applied force
Workdone = weight ×costeta ×length
Workdone=0•1×cos60° ×0•5
Workdone=0•1×0•5×0•5
Workdone=0.025joules
To solve this problem, we need to determine the work done in pulling the pendulum bob from its initial vertical position to the final position where the string makes an angle of 60° with the vertical.
Step 1: Understanding Work Done
The work done in pulling the bob is equal to the gain in gravitational potential energy (GPE) because the force is conservative.
The change in potential energy is given by:
W = mg \∆h
where:
m is the mass of the bob (not given directly, but we have its weight),
g is acceleration due to gravity (which is already incorporated into the weight),
∆h is the vertical height gained by the bob.
Step 2: Finding ∆h
The vertical height gain can be found using trigonometry.
Initially, the bob is at the lowest point, and its height is:
h initial = 0
At the final position, the bob's new height is the vertical component of the string’s length:
h final = L (1 - cos theta)
where:
L=50cm = 0.50 m (length of the string),
,theta=60°
.cos 60°= 1/2 or 0.5
h final = 0.50 * (1 - 0.5) = 0.50 * 0.5 = 0.25m
Thus, ∆h= 0.25m.
Step 3: Calculating Work Done
Since the weight of the bob is 0.1N, the work done is:
W = 0.1 * 0.25
W = 0.025J
Step 4: Choosing the Best Option
The correct answer is D. 0.025 J.
the formula h = L(1-cos theta) is commonly used to find the vertical displacement (∆h) of a pendulum bob when it swings to an angle theta from the vertical.
Explanation:
The bob is attached to a string of length of length L.
When at rest (hanging vertically), the bob’s height is at its lowest position.
When it swings to an angle theta , its new height is determined by the vertical component of L, which is L cos theta.
The vertical height gain ∆h is the difference between the total length and this vertical component:
∆ h = L - Lcos theta = L(1 - cos theta)
This formula is very useful for calculating gravitational potential energy change in pendulum motion or related problems.
The answers are correct, but the approach to solving it is wrong and misleading.
The correct formular to use would be:
Work done = mgh
Since the bob with a specific mass which was given in the question was displaced vertically (it's height was increased).
Using the illustration from the explanation which by the way is 100% correct, one can find for the vertical displacement, x, but where the error sets in is using f×d, taking the force as the weight given in the question, while the vertical displacement, x is the distance moved due to the force which is the weight given.
This is wrong because the vertical displacement is not due to the weight of the bob, but due to the variable horizontal force.
So, the correct formular would be
Work done = mgh
It's good to participate in dropping your views actually 
, but he real formula is Work done = MgR(1-Cos∅) = FR(1-cos∅)
No correct Option.
The distance needed is the distance away from the vertical =dsin60
Thus, workdone =F*(dsin60)
= 0.1*0.5*sin60
= 0.043J
No correct Option.
The distance needed is the distance awayA Bob of weight 0.1N hangs from a massless string of length 50cm. A variable horizontal force which increases from zero is applied to pull the Bob until the string makes angle of 60degree with the vertical. The work done is? from the vertical =dsin60
Thus, workdone =F*(dsin60)
= 0.1*0.5*sin60
= 0.043J
