Question:
A force on an object of mass \(100\ g\) is \((10\hat i+5\hat j)\ N\). The position of that object at \(t = 2s\) is \((a\hat i+b\hat j)\ m\) after starting from rest. The value of \(\frac ab\) will be _______ .
A force on an object of mass \(100\ g\) is \((10\hat i+5\hat j)\ N\). The position of that object at \(t = 2s\) is \((a\hat i+b\hat j)\ m\) after starting from rest. The value of \(\frac ab\) will be _______ .
Updated On: Jul 8, 2024
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Correct Answer: 2
Solution and Explanation
We know that,
\(\vec F = m\vec a\)
Where,
\(\vec a = 100\hat i+50\hat j\)
So,
\(\vec s = \frac {1}{2\vec a}t^2\)
\(\vec F = m\vec a\)
Where,
\(\vec a = 100\hat i+50\hat j\)
So,
\(\vec s = \frac {1}{2\vec a}t^2\)
\(\vec s = \frac 12(100\hat i+50\hat j)2^2\)
\(\vec s = 200\hat i+100\hat j\ m\)
Hence, \(a = 200\ m\) and \(b = 100\ m\)
Now, \(\frac ab = \frac {200}{100} = 2\)
\(\vec s = 200\hat i+100\hat j\ m\)
Hence, \(a = 200\ m\) and \(b = 100\ m\)
Now, \(\frac ab = \frac {200}{100} = 2\)
So, the answer is \(2\).
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Concepts Used:
Motion in a straight line
The motion in a straight line is an object changes its position with respect to its surroundings with time, then it is called in motion. It is a change in the position of an object over time. It is nothing but linear motion.
Types of Linear Motion:
Linear motion is also known as the Rectilinear Motion which are of two types:
- Uniform linear motion with constant velocity or zero acceleration: If a body travels in a straight line by covering an equal amount of distance in an equal interval of time then it is said to have uniform motion.
- Non-Uniform linear motion with variable velocity or non-zero acceleration: Not like the uniform acceleration, the body is said to have a non-uniform motion when the velocity of a body changes by unequal amounts in equal intervals of time. The rate of change of its velocity changes at different points of time during its movement.