1
JEE Main 2020 (Online) 9th January Morning Slot
+4
-1 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/IA of moment of inertia I0 of the system about an axis passing the centroid and about center of any of the spheres IA and perpendicular to the plane of the triangle is :
A
$${{13} \over {23}}$$
B
$${{23} \over {13}}$$
C
$${{15} \over {13}}$$
D
$${{13} \over {15}}$$
2
JEE Main 2020 (Online) 8th January Evening Slot
+4
-1
As shown in figure, when a spherical cavity (centered at O) of radius 1 is cut out of a uniform sphere of radius R (centered at C), the centre of mass of remaining (shaded) part of sphere is at G, i.e, on the surface of the cavity. R can be detemined by the equation : A
(R2 + R – 1) (2 – R) = 1
B
(R2 – R – 1) (2 – R) = 1
C
(R2 – R + 1) (2 – R) = 1
D
(R2 + R + 1) (2 – R) = 1
3
JEE Main 2020 (Online) 8th January Evening Slot
+4
-1
A uniform sphere of mass 500 g rolls without slipping on a plane horizontal surface with its centre moving at a speed of 5.00 cm/s. Its kinetic energy is :
A
8.75 × 10–3 J
B
1.13 × 10–3 J
C
8.75 × 10–4 J
D
6.25 × 10–4 J
4
JEE Main 2020 (Online) 8th January Morning Slot
+4
-1
Consider a uniform rod of mass M = 4m and length $$\ell$$ pivoted about its centre. A mass m moving with velocity v making angle $$\theta = {\pi \over 4}$$ to the rod's long axis collides with one end of the rod and sticks to it. The angular speed of the rod-mass system just after the collision is :
A
$${{3\sqrt 2 } \over 7}{v \over \ell }$$
B
$${3 \over 7}{v \over \ell }$$
C
$${3 \over {7\sqrt 2 }}{v \over \ell }$$
D
$${4 \over 7}{v \over \ell }$$
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