1
WB JEE 2024
+1
-0.25

A small sphere of mass m and radius r slides down the smooth surface of a large hemispherical bowl of radius R. If the sphere starts sliding from rest, the total kinetic energy of the sphere at the lowest point $$\mathrm{A}$$ of the bowl will be [given, moment of inertia of sphere $$=\frac{2}{5} \mathrm{mr}^2$$]

A
$$\mathrm{mg}(\mathrm{R}-\mathrm{r})$$
B
$$\frac{7}{10} \mathrm{mg}(\mathrm{R}-\mathrm{r})$$
C
$$\frac{2}{7}$$ mg $$(\mathrm{R}-\mathrm{r})$$
D
$$\frac{10}{7} \mathrm{mg}(\mathrm{R}-\mathrm{r})$$
2
WB JEE 2023
+1
-0.25

A mouse of mass m jumps on the outside edge of a rotating ceiling fan of moment of inertia I and radius R. The fractional loss of angular velocity of the fan as a result is,

A
$$\frac{m R^{2}}{I+m R^{2}}$$
B
$$\frac{I}{I+m R^{2}}$$
C
$$\frac{I-m R^{2}}{I}$$
D
$$\frac{I-m R^{2}}{I+m R^{2}}$$
3
WB JEE 2021
+2
-0.5
A uniform rod of length L pivoted at one end P is freely rotated in a horizontal plane with an angular velocity $$\omega$$ about a vertical axis passing through P. If the temperature of the system is increased by $$\Delta$$T, angular velocity becomes $${\omega \over 2}$$. If coefficient of linear expansion of the rod is $$\alpha$$($$\alpha$$ << 1), then $$\Delta$$T will be
A
$${1 \over \alpha }$$
B
$${1 \over 2\alpha }$$
C
$${1 \over 4\alpha }$$
D
$$\alpha$$
EXAM MAP
Medical
NEET