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(a) Initial angular velocity, $\omega$ = 40 rev/min, let the final angular velocity be $\omega$

Let the moment of inertia of the boy with hands stretched be I1 and

M.I. with folded hands be I2

Given I2 = (2/5) I1

Since no external force acts on the boy, the angular momentum will remain constant.

Hence I1 $\omega$ = I2 ${\omega }_1$ ,  ${\omega }_2$ I1/I2) x ${\omega }_1$ = (5/2) x 40 = 100 rev/min

(b) Kinetic energy Ev = (1/2)I ${\omega }_2$

Hence ( Final KE / Initial KE ) = (I2 ${\omega }_2=($ )/ (I1 ${\omega }_1$ ) = { (2/5) I1 x 100 x 100 } / { I1 x 40 x 40 }

= 2.5

Mass of the cylinder, m = 20 kg

Angular speed,  $\alpha$ = 100 rad/s

Radius of the cylinder, r = 0.25 m

The moment of inertia of the solid cylinder

I = (1/2) mr² = (1/2) x 20 x (0.25)² = 0.625 m²

Kinetic energy = (1/2)I ${\omega }_s$² = (1/2) x 0.625 x (100)² = 3125 J

Angular momentum, L = I ${\omega }_h$ = 0.625 x 100 = 62.5 Js

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The BBA students of the Gokul Global University are given full placement assistance. The students need to register themselves with the placement cell of the college in order to be able to sit for the placement drives held in the campus. The highest salary package offered during the placement drive at this university is INR 18 lakh. 

There are over 10 colleges in Shahdol that offer BSc courses. Pandit SN Shukla University is one of the options for the students. It offer BSc of three years in various specialisations. The selection criteria is merit-based. Apart from this, below are some of the other colleges as well that offers BSc in Shahdol:

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Mass of the car, m = 1800 kg

Distance between the front and rear axles, d = 1.8 m

Distance between C.G. and the front axle = 1.05 m

Let Rf and Rb be the force exerted from ground at front and rear axles respectively.

Rf + Rb = mg = 1800 x 9.8 N = 17640 N ……. (i)

For rotational equilibrium around C.G. we have Rf x 1.05 = Rb x (1.8 – 1.05)

R_f x 1.05 = R_b x 0.75

R_f/R_b = 0.75 / 1.05

R_f = 0.71 R_b ……. (ii)

From equation (i), we get

0.71 R_b + R_b = 17640

R_b = 10316 N

R_f = 7324 N

Therefore, force exerted on each front wheel = R_f/2 =7324/2 = 3662 N

Force exerted on each rear wheel, R_b/2 = 10316 / 2= 5158 N

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The Bachelor of Business Administration course is offered by the Gokul Global University. The duration of the course is spread across three years i.e., six semesters. In these six semesters students are also provided with opportunities of interships and project work. These are good for enhancing the practical knowledge.

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(i) A = {– 3, –2, –1, 0, 1, 2, 3, 4, 5, 6}

(ii) B = {1, 2, 3, 4, 5}

(iii) C = {17, 26, 35, 44, 53, 62, 71, 80}

(iv) x = Prime number which are divisor of 60

Factors of 60 are 1,2,3,4,5,6,10,12,15,20,30,60

Hence, x = 2, 3, 5

?D = {2, 3, 5}

(v) E = {T, R, I, G, O, N, M, E, Y}

(vi) F = {B, E, T, R}

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