1
JEE Main 2020 (Online) 7th January Evening Slot
+4
-1
Mass per unit area of a circular disc of radius $$a$$ depends on the distance r from its centre as $$\sigma \left( r \right)$$ = A + Br . The moment of inertia of the disc about the axis, perpendicular to the plane and assing through its centre is:
A
$$2\pi {a^4}\left( {{A \over 4} + {{aB} \over 5}} \right)$$
B
$$\pi {a^4}\left( {{A \over 4} + {{aB} \over 5}} \right)$$
C
$$2\pi {a^4}\left( {{{aA} \over 4} + {B \over 5}} \right)$$
D
$$2\pi {a^4}\left( {{A \over 4} + {B \over 5}} \right)$$
2
JEE Main 2020 (Online) 7th January Morning Slot
+4
-1
The radius of gyration of a uniform rod of length $$l$$, about an axis passing through a point $${l \over 4}$$ away from the centre of the rod, and perpendicular to it, is :
A
$${1 \over 8}l$$
B
$${1 \over 4}l$$
C
$$\sqrt {{7 \over {48}}} l$$
D
$$\sqrt {{3 \over 8}} l$$
3
JEE Main 2020 (Online) 7th January Morning Slot
+4
-1
As shown in the figure, a bob of mass m is tied by a massless string whose other end portion is wound on a fly wheel (disc) of radius r and mass m. When released from rest the bob starts falling vertically. When it has covered a distance of h, the angular speed of the wheel will be:
A
$$r\sqrt {{3 \over {2gh}}}$$
B
$$r\sqrt {{3 \over {4gh}}}$$
C
$${1 \over r}\sqrt {{{4gh} \over 3}}$$
D
$${1 \over r}\sqrt {{{2gh} \over 3}}$$
4
JEE Main 2019 (Online) 12th April Morning Slot
+4
-1
A circular disc of radius b has a hole of radius a at its centre (see figure). If the mass per unit area of the disc varies as $$\left( {{{{\sigma _0}} \over r}} \right)$$ , then the radius of gyration of the disc about its axis passing through the centre is:
A
$$\sqrt {{{{a^2} + {b^2} + ab} \over 2}}$$
B
$$\sqrt {{{a + b} \over 3}}$$
C
$$\sqrt {{{{a^2} + {b^2} + ab} \over 3}}$$
D
$$\sqrt {{{a + b} \over 2}}$$
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