Question Bank Directory

An energy of $484 \text{ J}$ is spent in increasing the speed of a flywheel from $60 \text{ rpm}$ to $360 \text{ rpm}$. The moment of inertia of the flywheel is:

A system consists of three masses $m_1$, $m_2$ and $m_3$ connected by a string passing over a pulley P. The mass $m_1$ hangs freely and $m_2$ and $m_3$ are on a rough horizontal table (the coefficient of friction = $\mu$). The pulley is frictionless and of negligible mass. The downward acceleration of mass $m_1$ is: (Assume $m_1=m_2=m_3=m$)

A plank with a box on it at one end is gradually raised about the other end. As the angle of inclination with the horizontal reaches $30^\circ$, the box starts to slip and slides $4.0 \text{ m}$ down the plank in $4.0 \text{ s}$. The coefficients of static and kinetic friction between the box and the plank will be, respectively:

A hollow sphere of diameter $0.2 \text{ m}$ and mass $2 \text{ kg}$ is rolling on an inclined plane with velocity $v = 0.5 \text{ m/s}$. The kinetic energy of the sphere is:

A force $\vec{F} = \alpha\hat{i} + 3\hat{j} + 6\hat{k}$ is acting at a point $\vec{r} = 2\hat{i} - 6\hat{j} - 12\hat{k}$. The value of $\alpha$ for which angular momentum is conserved about the origin is:

In a regular octahedral molecule, $MX_{6}$, the number of $X–M–X$ bonds at 180º is:

The upper half of an inclined plane of inclination $\theta$ is perfectly smooth while the lower half is rough. A block starting from rest at the top of the plane will again come to rest at the bottom if the coefficient of friction between the block and lower half of the plane is given by:

The distance covered by a body of mass $5 \text{ g}$ having linear momentum $0.3 \text{ kg m/s}$ in $5 \text{ s}$ is:

From a disc of radius $R$ and mass $M$, a circular hole of diameter $R$, whose rim passes through the centre is cut. What is the moment of inertia of the remaining part of the disc about a perpendicular axis, passing through the centre?

A string is wrapped along the rim of a wheel of the moment of inertia $0.10 \text{ kg-m}^2$ and radius $10 \text{ cm}$. If the string is now pulled by a force of $10 \text{ N}$, then the wheel starts to rotate about its axis from rest. The angular velocity of the wheel after $2 \text{ s}$ will be:

The angular acceleration of a body moving along the circumference of a circle is:

A copper rod of $88 \text{ cm}$ and an aluminium rod of an unknown length have an equal increase in their lengths independent of an increase in temperature. The length of the aluminium rod is: ($\alpha_{\text{Cu}} = 1.7 \times 10^{-5} \text{ K}^{-1}$ and $\alpha_{\text{Al}} = 2.2 \times 10^{-5} \text{ K}^{-1}$)

Which one of the following vitamins is water-soluble?

ABC is an equilateral triangle with O as its centre. $\vec{F}_1$, $\vec{F}_2$ and $\vec{F}_3$ represent three forces acting along the sides AB, BC and AC respectively. If the total torque about O is zero then the magnitude of $\vec{F}_3$ is:

A person of mass $60 \text{ kg}$ is inside a lift of mass $940 \text{ kg}$ and presses the button on the control panel. The lift starts moving upwards with an acceleration of $1.0 \text{ m/s}^2$. If $g=10 \text{ m/s}^2$, the tension in the supporting cable is:

Three blocks with masses $m$, $2m$, and $3m$ are connected by strings as shown in the figure. After an upward force $F$ is applied on block $m$, the masses move upward at constant speed $v$. What is the net force on the block of mass $2m$? ($g$ is the acceleration due to gravity)

A particle of mass $m$ is projected with velocity $v$ making an angle of $45^\circ$ with the horizontal. When the particle lands on the level ground, the magnitude of the change in its momentum will be:

Consider a thin circular ring (A), a circular disc (B), a hollow cylinder (C) and a solid cylinder (D) of the same radii $R$ and of the same masses. If $I_A$, $I_B$, $I_C$ and $I_D$ are their moments of inertia about the axis shown, then choose the correct answer from the options given below:

If the initial tension on a stretched string is doubled, then the ratio of the initial and final speeds of a transverse wave along the string is:

A bullet is fired from a gun at the speed of $280 \text{ m s}^{-1}$ in the direction $30^{\circ}$ above the horizontal. The maximum height attained by the bullet is: ($g=9.8 \text{ m s}^{-2}, \sin 30^{\circ}=0.5$)