1
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
2
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
3
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
$${4 \over 7}{v \over \ell }$$
4
JEE Main 2020 (Online) 8th January Morning Slot
+4
-1
The coordinates of centre of mass of a uniform flag shaped lamina (thin flat plate) of mass 4kg. (The coordinates of the same are shown in figure) are :
A
(0.75m, 1.75m)
B
(1m, 1.75m)
C
(0.75m, 0.75m)
D
(1.25m, 1.50m)
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