*Let *~~Us~~ YOU* Solve Physics JEE (MAIN) 2018 Physics Paper*

~~Us~~

In a series of blogs, we @ www.PhysicsAcademyOnline.com encourage our readers (students preparing for engineering and medical entrance exams) to solve *on their own* Physics questions from recent examination papers. We believe, and we want our readers to believe, a solid grip on the theories and quick problem-solving skill are the success keys to a high rank in a keenly contested exam. Presently, we are discussing JEE (Main) 2018, Paper-1, held on 08 April 2018.

** Question 8:** A particle is moving with a constant speed in a circular orbit of radius R under a central force inversely proportional to the n

^{th}power of R. If the period of revolution of the particle is T, then:

(1) T*∝ *R ^{3/2} for any n

(2) T*∝ *R^{n/2 + 1}

(3) T*∝ *R^{(n + 1)/2}

(4) T*∝ *R^{n/2}

Using the condition given in the question, express the central force, F_{c} , in terms of orbit radius, R. What is the acceleration of the particle? Discussed in detail here: *Chapter Name – Mechanics; Category – Basic; Topic Name – Circular Motion; Video Name – Derivation of Centripetal Acceleration.*

For an alternative expression, you may see: *Chapter Name – Mechanics; Category – Basic; **Topic Name – Circular Motion; Video Name – Relations between Linear and Angular Quantities.*

Use Newton’s second law to express F_{c} . Compare with its earlier expression. How do you introduce time period, T, in your last result? The relevant formula is here: *Chapter Name – Mechanics; Category – Basic; **Topic Name – Circular Motion; Video Name – Angular Quantities in Circular Motion.*

Little rearrangement leads you to to the correct option.

** Question 9:** A solid sphere of radius r, made of a soft material of bulk modulus K, is surrounded by a liquid in a cylindrical container. A massless piston of area “a” floats on the surface of the liquid, covering the entire cross section of the container. When a mass m is placed on top of the piston to compress the liquid, the fractional decrement in the radius of the sphere, │dr/r│, is:

(1) Ka/mg (2) Ka/3mg (3) mg/3Ka (4) mg/Ka

What is the formula for bulk modulus, K, of a material? The one using calculus notation is preferred. Watch the lecture: * Chapter Name – Elasticity and Fluid Mechanics; Category –Basic; **Topic Name – Elasticity; Video Name – Bulk Modulus & Relations among Elastic Constants.*

As the mass m is placed on the piston, what is the differential change in pressure? Therefore, what is the fractional change in volume of the sphere?

Now for a sphere, volume, V = 4 *π*r^{3}/3. Taking logarithm on both sides, ln V = ln (4*π*/3) + 3 ln r. Differentiating both sides, dV/V = 3 dr/r. The fractional change in radius follows. By the way, how is “fractional decrement” different from “fractional change”?