Try this beautiful problem, useful for Physics Olympiad based on Two Blocks on an Inclined Plane.
The Problem:
Two blocks of masses (4kg) and (8kg) are connected by a string and slide down a (30^\circ) inclined plane. The coefficient of kinetic friction between the (4Kg) block and the plane is (0.25); that between the (8Kg) block and the plane is (0.35).
(a) Calculate the acceleration of each block.
(b) Calculate the tension in the string.
Discussion:
Since the larger block has the larger coefficient of friction it will need to be pulled down the plane.
For the small block, $$ 4(sin30^\circ-(0.25)cos30^\circ)-T=4a$$
$$\Rightarrow 4a=11.11N-t$$
For larger block, $$ 15.44+T=8a$$
Now, adding the two relations $$ 26.55N=12a$$
$$ a=2.21m/s^2$$
We can find the tension (T=2.27N)
In 2026, the following Cheenta students have been successful for Indian Statistical Institute's M.Stat Entrance. They ranked within the first 50 in the entire country in these entrances. I.S.I. M.Stat Entrance
In 2026, the following Cheenta students have been successful for Indian Statistical Institute's B.Stat Entrance and Chennai Mathematical Institute's B.Sc. Math Entrance. They ranked within the first 200 in the entire country in these entrances. Most of these students attended the problem solving workshops regularly, which happen 5 days every week. CMI B.Sc. Math Entrance […]
In 2025, 8 students from Cheenta Academy cracked the prestigious Regional Math Olympiad. In this post, we will share some of their success stories and learning strategies. The Regional Mathematics Olympiad (RMO) and the Indian National Mathematics Olympiad (INMO) are two most important mathematics contests in India.These two contests are for the students who are […]
Cheenta Academy proudly celebrates the success of 27 current and former students who qualified for the Indian Olympiad Qualifier in Mathematics (IOQM) 2025, advancing to the next stage — RMO. This accomplishment highlights their perseverance and Cheenta’s ongoing mission to nurture mathematical excellence and research-oriented learning.