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A uniform rod $\text{AB},4\text{m}$ long and weight $12\text{kg}$, is supported at end A, with a $6\text{kg}$ lead weight at B. The rod floats as shown in figure with one-half of its length submerged. The buoyant force on the lead mass is negligible as it is of negligible volume. Find the tension in the cord and the total volume of the rod.

Find the ratio of tensions $T_1$ and $T_2$ for the figure shown.

The masses of $4\text{kg}$ and $5\text{kg}$ are connected by a string passing over a frictionless pulley and are kept on a frictionless table as shown in the figure. The acceleration of $5\text{kg}$ mass is

Find the maximum and minimum values of function $y=2x^3-15x^2+36x+11$

The vibration of a string fixed at both ends are described by $y=2sin\left(\pi x\right)sin\left(100\pi t\right)$ where Y is in mm, x is in cm and t is in second. Then

Find the integral of the given function w.r.t x

$y=\frac{1}{\sqrt[3]{3x^2}}$

Locus of the poles of focal chords of a parabola is of parabola

If the volume of the given mass of a gas is increased four times, the temperature is raised from ${27}^{o}C$ to ${127}^{o}C$. The elasticity will become

The centre of mass of a semi-circular ring lies $5\text{cm}$ above the centre of the semi-circle. What is the circumference of the ring?

Below is the graph for $\tau =2\sin \theta$. calculate work done by the torque till $\theta =\pi .$

A block of weight 200 N is pulled along a rough horizontal surface at a constant speed by a force of 100 N acting at an angle of ${30}^{\circ }$ above the horizontal. The coefficient of friction between the block and the surface is

The $E-r$ curve for an infinite linear charge distribution will be

Find the velocity of the hanging block if the velocities of the free ends of the rope are as indicated in the figure. Assume that the pulleys are frictionless and string is inextensible.

The momentum $P$ and kinetic energy $E$ of a body of mass $m$ are related as:

Find the density of a metallic body which floats at the interface of mercury of specific gravity $13.6$ and water such that $31.75\%$ of its volume is submerged in mercury and $68.25\%$ in water.

When a $24\text{V}$ battery is connected to a resistor, the current in it is $0.4\text{A}$. What will be the current through it when it is connected to a battery of $6\text{V}?$

A beam of light propagating in medium A with index of refraction n (A)passes across an interface into medium B with index of refraction n(B). The angle of incidence is greater than the angle of refraction; v(A) and v(B) denotes the speed of light in A and B. Then which of the following is true

A compass needle is free to turn in a horizontal plane is placed at the centre of a circular coil of $30$ turns and radius $12\text{cm}$. The coil is in a vertical plane, making an angle of ${45}^{\circ }$ with the magnetic meridian. When the current in the coil is $0.35\text{A}$, the needle points west to east. Find the horizontal component of the earth's magnetic field at the location.

The household supply of electricity is at 220 V (rms value) and 50 Hz. Find the peak voltage and the least possible time in which the voltage can change from the rms value to zero

Analyze the given data:



The function that models the given data is.

Figure shows two blocks in contact and sliding down the inclined surface of inclination ${30}^{\circ }$. Coefficient of friction between the block of mass $4\text{kg}$ and the inclined plane is ${\mu }_1=0.3$ and that between the block of mass $2\text{kg}$ and the inclined plane is ${\mu }_2=0.20$. Assume coefficients of static and kinetic friction to be equal. Find the acceleration of $2\text{kg}$ block. Take $g=10{\text{m/s}}^2$.

Give that the time period T of ossilation of a gas bubble from an explosion under water depends uopon P, D and E ehere P is the static pressure, D is the density of water and E is the total energy of explosion, find dimensionally the relation of T.

Calculate the amount of heat required to convert 1.00 kg of ice at -10°C at normal pressure to steam at 100°C. Specific heat capacity of ice = 2100 J kg⁻¹ K⁻¹ , latent heat of fusion of ice = 3.36 × 10⁵ J kg⁻¹ , specific heat capacity of water = 4200 J kg ⁻¹ K⁻¹ and latent heat of vaporization of water = 2.25 × 10⁶ J kg⁻¹

A uniform ring of mass $m$ and radius $R$ is rolling down a rough inclined plane which makes an angle ${37}^{\circ }$ with the horizontal. If the friction is sufficient for pure rolling, then fricition force on ring is

A body starts from the origin and moves along
the x-axis such that the velocity at any instant is given by (4t³-
2t), where t is in second and velocity in m/s. What is the acceleration of the
particle, when it is 2m from the origin on positive side?

A hydrogen atom contains one proton and one electron. It may be assumed that the electron revolves in a circle of radius 0.53 angstrom $(1angstrom={10}^{-10}$ m and is abbreviated as $\stackrel{\circ }{A}$ with the proton at the centre. Teh hydrogen atom is said to be in the ground state in this case. Find th magnitude of the electric force between the proton and the electron of a hydrogen atom in its ground state.