JEE Main 2020 (Online) 9th January Evening Slot | Rotational Motion Question 88 | Physics

JEE Main 2020 (Online) 9th January Evening Slot

MCQ (Single Correct Answer)

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A spring mass system (mass m, spring constant k and natural length $$l$$) rest in equilibrium on a horizontal disc. The free end of the spring is fixed at the centre of the disc. If the disc together with spring mass system, rotates about it's axis with an angular velocity $$\omega $$, (k $$ \gg m{\omega ^2}$$) the relative change in the length of the spring is best given by the option :

$${{m{\omega ^2}} \over {3k}}$$

$${{m{\omega ^2}} \over k}$$

$${{2m{\omega ^2}} \over k}$$

$$\sqrt {{2 \over 3}} \left( {{{m{\omega ^2}} \over k}} \right)$$

JEE Main 2020 (Online) 9th January Evening Slot

MCQ (Single Correct Answer)

-1

A rod of length L has non-uniform linear mass
density given by $$\rho $$(x) = $$a + b{\left( {{x \over L}} \right)^2}$$ , where a
and b are constants and 0 $$ \le $$ x $$ \le $$ L. The value
of x for the centre of mass of the rod is at :

$${3 \over 2}\left( {{{a + b} \over {2a + b}}} \right)L$$

$${4 \over 3}\left( {{{a + b} \over {2a + 3b}}} \right)L$$

$${3 \over 4}\left( {{{2a + b} \over {3a + b}}} \right)L$$

$${3 \over 2}\left( {{{2a + b} \over {3a + b}}} \right)L$$

JEE Main 2020 (Online) 9th January Evening Slot

MCQ (Single Correct Answer)

-1

A uniformly thick wheel with moment of inertia I and radius R is free to rotate about its centre of mass (see fig). A massless string is wrapped over its rim and two blocks of masses m₁ and m₂ (m₁ $$ > $$ m₂) are attached to the ends of the string. The system is released from rest. The angular speed of the wheel when m₁ descents by a distance h is : JEE Main 2020 (Online) 9th January Evening Slot Physics - Rotational Motion Question 89 English

JEE Main 2020 (Online) 9th January Evening Slot Physics - Rotational Motion Question 89 English

$${\left[ {{{2\left( {{m_1} + {m_2}} \right)gh} \over {\left( {{m_1} + {m_2}} \right){R^2} + I}}} \right]^{{1 \over 2}}}$$

$${\left[ {{{{m_1} + {m_2}} \over {\left( {{m_1} + {m_2}} \right){R^2} + I}}} \right]^{{1 \over 2}}}gh$$

$${\left[ {{{\left( {{m_1} - {m_2}} \right)} \over {\left( {{m_1} + {m_2}} \right){R^2} + I}}} \right]^{{1 \over 2}}}gh$$

$${\left[ {{{2\left( {{m_1} - {m_2}} \right)gh} \over {\left( {{m_1} + {m_2}} \right){R^2} + I}}} \right]^{{1 \over 2}}}$$

JEE Main 2020 (Online) 9th January Morning Slot

MCQ (Single Correct Answer)

-1

JEE Main 2020 (Online) 9th January Morning Slot Physics - Rotational Motion Question 94 English

Three solid spheres each of mass m and diameter d are stuck together such that the lines connecting the centres form an equilateral triangle of side of length d. The ratio I₀/I_A of moment of inertia I₀ of the system about an axis passing the centroid and about center of any of the spheres I_A and perpendicular to the plane of the triangle is :

$${{13} \over {23}}$$

$${{23} \over {13}}$$

$${{15} \over {13}}$$

$${{13} \over {15}}$$

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