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A small sector is cut from a uniform circular disc of radius $1\text{m}$. The sector subtends an angle ${90}^{\circ }$ at the center of the disc. This sector has mass $0.16\text{kg}$ and it is made to rotate about a line perpendicular to its plane and passing through the center of the original disc. Its moment of inertia about the axis of rotation is,

A $10\text{cm}$ long rod carries a charge of $+50\mu \text{C}$ distributed uniformly along its length. Find the magnitude of the electric field at a point $10\text{cm}$ from both the ends of the rod.

A magnetic flux of $5.5\times {10}^{-4}\text{Wb}$ is linked with a coil of resistance $10\Omega$ and $1\text{turn}$. If the magnetic flux is changed to $5\times {10}^{-4}\text{Wb}$ in $0.1\text{sec}$, the induced charge in the coil is,

A scooter company gives the following specifications about its product.

Weight of the scooter- 95 kg

Maximum speed – 60 kh/h

Maximum engine power – 3.5 hp

Pick up time to get the maximum speed – 5 s

Check the validity of these specifications.

At an instant particle A is at origin and moving with constant velocity $(3\hat{i}+4\hat{j})$ m/s and particle B is at (4, 4)m and moving with constant velocity $(4\hat{i}-3\hat{j})$ m/s. Then at this instant

An insect crawls up a hemispherical surface very slowly (see the figure). The coefficient of friction between the surface and the insect is $\frac{1}{3}$. If the joining the centre of the hemispherical surface to the insect makes an angle $\alpha$ with the vertical, the maximum possible value of $\alpha$ is given

The binding energy per nucleon for a $\text{deuteron}$ and an $\alpha -\text{particle}$ is $x_1$ and $x_2$ respectively. The energy $Q$ released in the reaction ${}_1{\text{H}}^2{+}_1{\text{H}}^2{\to }_2{\text{He}}^4+Q,$ is

Which of these situations shown are in stable equilibrium?

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A spring of natural length $2x\text{m}$ is elongated such that its extension is twice its original length. If the force constant($k$) of spring is $8\text{N/m}$, the potential energy ($\text{J}$) stored in the spring is:

A disc is rolling without slipping on a horizontal surface with C, as its centre, and Q and P the two points equidistant from

C. Let $v_P,v_Q$ and $v_C$ be the magnitudes of velocities of points $P$, $Q$ and $C$ respectively, then

Turpentine oil is flowing through a tube of length ${}^{\prime }{l}^{\prime }$ and radius ${}^{\prime }{r}^{\prime }$ . The pressure difference between the two ends of tube is $P$. The viscosity of oil is given by $\eta =\frac{P(r^2-x^2)}{4vl}$, where $v$ is velocity of oil at a radial distance '$x$' from the axis of tube. The dimensions of $\eta$ are

Eight identical capacitor of capacitance $C$ each are connected along edge of a pyramid having square base, $\text{ABCD}$ as shown. Equivalant capacitance across $\text{A}$ and $\text{O}$ is

The first ionisation potential in electron volts of nitrogen and oxygen atoms are respectively given by

The graph shown was obtained from experimental measurements of the period of oscillations T for different masses M placed in the scale pan on the lower end of the spring balance. The most likely reason for the line not passing through the origin is that the

What were the forces involved in the calculations made by Millikan in his oil drop experiment

Four particles, each of mass $M$, move along a circle of radius $R$ under the action of their mutual gravitational attraction. The speed of each particle is

Find the maximum force that should act on the $7\text{kg}$ body for the system to accelerate together with $1{\text{m/s}}^2$. Take $g=10{\text{m/s}}^2$.

A source emitting a sound of frequency v is placed at a large distance from an observer. The source starts moving towards the observer with a uniform acceleration a. Find the frequency heard by the observer corresponding to the wave emitted just after the source starts. The speed of sound in the medium is v.

Two identical conducting spheres carrying different charges attract each other with a force F when placed in air medium at a distance d apart. The spheres are brought into contact and then taken to their original positions. Now the two spheres repel each other with a force whose magnitude is equal to that of the initial attractive force. The ratio between initial charges on the spheres is

An observer approaches towards a stationary source of sound at constant velocity and recedes away at the same speed. The graph of wavelength observed with time is:

A triangular open channel has a vortex angle of ${90}^{\circ }$ and carries flow at a critical depth of 0.3 m. The discharge in the channel is

Find the acceleration of the block of mass $2m$ as shown in the figure. (Strings are massless and inextensible)

Figure 5.18 shows a man standing stationary with respect to a horizontal conveyor belt that is accelerating with 1 m s^–2. What is the net force on the man? If the coefficient of static friction between the man’s shoes and the belt is 0.2, up to what acceleration of the belt can the man continue to be stationary relative to the belt? (Mass of the man = 65 kg.)

Figure 5.18