Two masses \(M_1\) and \(M_2\) are tied together at the two ends of a light inextensible string that passes over a frictionless pulley. When the mass \(M_2\) is twice that of \(M_1\), the acceleration of the system is \(a_1\). When the mass \(M_2\) is thrice that of \(M_1\), the acceleration of the system is \(a_2\). The ratio \(\frac{a_1}{a_2}\) will be
- \(\frac{1}{3}\)
- \(\frac{2}{3}\)
- \(\frac{3}{2}\)
- \(\frac{1}{2}\)
The Correct Option is B
Solution and Explanation
the acceleration ratio of two masses:
\(a_1 = \frac{M_2-M_1}{M_2+M_1} \times g \)
= \(\frac{2M_1-M_1}{3M_1} \times g\)
then, \(a_2 = \frac{3M_1-M_1}{4M_1} \times g = \frac{g}{2}\)
therefore, \(\frac{a_1}{a_2} = \frac{\frac{g}{3}}{\frac{g}{2}}\)
= \(\frac{2}{3}\)
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Concepts Used:
Friction
Friction is defined as the resistance offered by the surfaces that are in contact when they move past each other.
Types of Friction
There are four categories of Friction- static friction, sliding friction, rolling friction, and fluid friction.
Sliding Friction
In Sliding Friction, the weight of the sliding object calculates the amount of sliding friction present between the two objects. The sliding friction is supposed to be greater as the pressure exerted by the heavy object on the surface it slides over is comparably more.
Rolling Friction
Friction between a circular object and the surface is called as Rolling Friction. It is required to overcome sliding friction is more than the force required to overcome the rolling friction.
Static Friction
Friction that keeps an object at rest without initiating any relative motion between the body and the surface is termed as Static Friction. For example, a parked car resting on the hill, a hanging towel on the rack. The maximum force of static friction is directly proportional to the normal force.
Fluid Friction
Fluid Friction is the kind of friction that is exerted by the fluid on the object that is moving through a fluid.