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A certain force applied to mass m1 given it an acceleration of 10 ms–2. The same force applied to mass m2 gives it an acceleration of 15ms–2. If the two masses are joined together and the same force is applied to the combination, the acceleration will be
- a)6 ms–2
- b)3 ms–2
- c)9 ms–2
- d)12 ms–2
Correct answer is option 'A'. Can you explain this answer?
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A certain force applied to mass m1 given it an acceleration of 10 ms&#...
Acceleration is directly proportional to the force applied and inversely proportional to the mass. Mathematically, we can express this relationship using Newton's second law of motion:
F = ma
where F is the force applied, m is the mass, and a is the acceleration.
Given that the force applied to mass m1 gives it an acceleration of 10 m/s^2, we can write:
F = m1 * 10
Similarly, the force applied to mass m2 gives it an acceleration of 15 m/s^2:
F = m2 * 15
If the two masses are joined together, the total mass is the sum of m1 and m2:
m_total = m1 + m2
Now, let's find the acceleration when the same force is applied to the combination.
Since the force is the same, we can equate the expressions for force in terms of m1 and m2:
m1 * 10 = m2 * 15
Now, we can solve for m1 in terms of m2:
m1 = (m2 * 15) / 10
Substituting this expression for m1 into the total mass equation:
m_total = ((m2 * 15) / 10) + m2
m_total = (3m2/2) + m2
m_total = (5m2/2)
Now, we can rewrite the equation F = m_total * a in terms of m2:
F = (5m2/2) * a
Since the force is the same, we can also express the force in terms of m_total:
F = m_total * a_total
Equating these two expressions for force, we get:
(5m2/2) * a = m_total * a_total
Now, we can solve for a_total in terms of m2 and a:
a_total = (5m2/2) * a / m_total
Substituting the expression for m_total:
a_total = (5m2/2) * a / (5m2/2)
The m2 terms cancel out, leaving us with:
a_total = a
Therefore, the acceleration of the combined masses is equal to the acceleration of each individual mass. In this case, since the acceleration of each individual mass is 10 m/s^2, the acceleration of the combined masses is also 10 m/s^2.
Therefore, the correct answer is option A: 6 m/s^2.
F = ma
where F is the force applied, m is the mass, and a is the acceleration.
Given that the force applied to mass m1 gives it an acceleration of 10 m/s^2, we can write:
F = m1 * 10
Similarly, the force applied to mass m2 gives it an acceleration of 15 m/s^2:
F = m2 * 15
If the two masses are joined together, the total mass is the sum of m1 and m2:
m_total = m1 + m2
Now, let's find the acceleration when the same force is applied to the combination.
Since the force is the same, we can equate the expressions for force in terms of m1 and m2:
m1 * 10 = m2 * 15
Now, we can solve for m1 in terms of m2:
m1 = (m2 * 15) / 10
Substituting this expression for m1 into the total mass equation:
m_total = ((m2 * 15) / 10) + m2
m_total = (3m2/2) + m2
m_total = (5m2/2)
Now, we can rewrite the equation F = m_total * a in terms of m2:
F = (5m2/2) * a
Since the force is the same, we can also express the force in terms of m_total:
F = m_total * a_total
Equating these two expressions for force, we get:
(5m2/2) * a = m_total * a_total
Now, we can solve for a_total in terms of m2 and a:
a_total = (5m2/2) * a / m_total
Substituting the expression for m_total:
a_total = (5m2/2) * a / (5m2/2)
The m2 terms cancel out, leaving us with:
a_total = a
Therefore, the acceleration of the combined masses is equal to the acceleration of each individual mass. In this case, since the acceleration of each individual mass is 10 m/s^2, the acceleration of the combined masses is also 10 m/s^2.
Therefore, the correct answer is option A: 6 m/s^2.
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A certain force applied to mass m1 given it an acceleration of 10 ms&#...
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A certain force applied to mass m1 given it an acceleration of 10 ms–2. The same force applied to mass m2 gives it an acceleration of 15ms–2. If the two masses are joined together and the same force is applied to the combination, the acceleration will bea)6 ms–2b)3 ms–2c)9 ms–2d)12 ms–2Correct answer is option 'A'. Can you explain this answer?
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A certain force applied to mass m1 given it an acceleration of 10 ms–2. The same force applied to mass m2 gives it an acceleration of 15ms–2. If the two masses are joined together and the same force is applied to the combination, the acceleration will bea)6 ms–2b)3 ms–2c)9 ms–2d)12 ms–2Correct answer is option 'A'. Can you explain this answer? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about A certain force applied to mass m1 given it an acceleration of 10 ms–2. The same force applied to mass m2 gives it an acceleration of 15ms–2. If the two masses are joined together and the same force is applied to the combination, the acceleration will bea)6 ms–2b)3 ms–2c)9 ms–2d)12 ms–2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A certain force applied to mass m1 given it an acceleration of 10 ms–2. The same force applied to mass m2 gives it an acceleration of 15ms–2. If the two masses are joined together and the same force is applied to the combination, the acceleration will bea)6 ms–2b)3 ms–2c)9 ms–2d)12 ms–2Correct answer is option 'A'. Can you explain this answer?.
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