NSEP 2015 Problem 9 | Pulley problem

Try this problem on pulley problem on inclined plane from NSEP 2015 Problem 9.

NSEP 2015-16 ~ Problem 9

Maases $m_1$ and $m_2$ are connected to a string passing over a pulley as shown. Mass $m_2$ starts from rest and falls through a distance $d$ in time t. Now, by interchanging the masses the time required for $m_1$ to fall through the same distance is $2t$. Therefore, the ratio of masses $m_2 : m_1$

a) $\frac{2}{3}$ b) $\frac{3}{2}$ c) $\frac{5}{2}$ d) $\frac{4}{3}$

$m_1$ and $m_2$ are interchanged from real problem

Key Concepts

Newton's Laws of Motion

Idea of accelerations, velocity and displacement

Suggested Book | Source | Answer

Concept of Physics H.C. Verma

University Physics by H. D. Young and R.A. Freedman

Fundamental of Physics D. Halliday, J. Walker and R. Resnick

National Standard Examination in Physics(NSEP) 2015-2016

Option-(b) $\frac{3}{2}$

Try with Hints

We know at the beginning the blocks have zero velocities. Using the relation $s= ut+\frac{1}{2}at^2$, we can find the relation between the accelerations for two cases (i.e., when they are interchanged).

Knowing the accelerations we can now use the second law of newton to find the ratio of masses.

From the first hint,

$$ \frac{1}{2}a_1t^2 = \frac{1}{2}a_2 (2t)^2 \to a_1 =4 a_2 $$

Now, we find the value of $a_1$ and $a_2$ using $a = \frac{F}{M}$

$$ \frac{m_2 g - m_1g \sin(30)}{m1+m_2} = 4 \frac{m_1 g - m_2g \sin(30)}{m1+m_2} $$

Rearranging this expression and using $\sin(30) = \frac{1}{2}$,

This gives, $\frac{m_2}{m_1} = \frac{3}{2}$

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Related Program

Physics Olympiad Program at Cheenta

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NSEP 2015 Problem 8 | One Dimensional Motion

Try out this problem on one dimensional motion(Kinematics) from National Standard Examination in Physics 2015-2016.

NSEP 2015-16 ~ Problem 8

A car moving along a straight road at a speed of u m/s applies brakes at $t=0$ seconds. The ratio of distances travelled by the car during $3^{rd}$ and $8^{th}$ seconds is $15:13$. The car covers a distance of $0.25m$ in the last second of it's travel. Therefore, the acceleration a (in $m/s^2$) and the speeed u($m/s$) of the car are respectively,

a) $-0.1,16$

b) $-0.2,12$

c) $-0.5,20$

d) $-0.1,16$

Key Concepts

Basic Equation of motions

Idea of accelerations, velocity and displacement

Suggested Book | Source | Answer

Concept of Physics H.C. Verma

University Physics by H. D. Young and R.A. Freedman

Fundamental of Physics D. Halliday, J. Walker and R. Resnick

National Standard Examination in Physics(NSEP) 2015-2016

Option-(c) $-0.5,20$

Try with Hints

We know that displacement in $t$ sec is given by,

$$ s = ut +\frac{1}{2} a t^2$$

where $u$ is the initial velocity and $a$ is the acceleration. This will be negative for deceleration.

Using this idea we can just find the expression for the displacement in the $n^{th}$ second, for which the information is given to us.

Also, the car come to rest and at the second second it travels a distance of $0.25m$. WE can think it in opposite manner that with an acceleration of $a$ and initial velocity $0m/s$, the car moves a distance of $0.25m$ , hence,

$$0.5 =\frac{1}{2} a (1^2)$$

So, the displacement in $n^{th}$ second is,

$$ s_1 = ut+\frac{1}{2} a n^2 $$

and for the $(n-1)^{th}$ second the displacement is,

$$ s_2= ut+\frac{1}{2} a (n-1)^2 $$

Hence, we have

$$ s_n = s_1-s_2 = u + a(n-\frac{1}{2}) $$

we have,

$$ \frac{15}{13} = \frac{s_3}{s_8} = \frac{u-\frac{5a}{2}}{u - \frac{15a}{2}} $$

Also we have $0.5 =\frac{1}{2} a (1^2)$

Solving this two gives us $a = 0.25m/s^2 $. Putting this in first equation gives us $u = 20 m/s $.

Other useful links

Related Program

Physics Olympiad Program at Cheenta

Subscribe to Cheenta at Youtube