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What should be the maximum value of $M$ so that the $4\text{kg}$ block does not slip over the $5\text{kg}$ block: (Take $g=10{\text{m/s}}^2)$

1. 300

London forces are also known as

The relation between time and displacement of a moving object is given as t= ax² + bx, where a, b are constants. Prove that the acceleration of the body is( -2av³)

What is the value of 1 Wb/m² in terms of G? Also specify the SI units used like G, T and Wb.

Two bodies M and N of equal masses are suspended from two separate massless springs of spring constants $k_1$ and $k_2$ respectively. If the two bodies oscillate vertically such that their maximum velocities are equal, the ratio of the amplitude of vibration of M to that of N is

Choose the correct statements(s) from the following:

A ball drops from the ceiling of the room, and after rebounding twice from the floor, reaches a height equal to half that of ceiling. Find the coefficient of restitution?

Two plates of a capacitor of the area $100{\text{cm}}^2$ are separated by a distance of $8\text{cm}$, and charged by a battery of emf $56\text{V}$. If the separation is increased by $8.5\text{mm}$, then the new capacitance will be

A particle of mass $m$ is fixed to one end of a light of a light spring having force constant $k$ and unstretched length $l$. The other end is fixed. The system is given an angular speed $\omega$ about the fixed end of the spring, such that it rotates in a circle in gravity free space. Then the stretch in the spring is

What is the value of linear velocity, if$\overrightarrow{\omega }=3\hat{i}-4\hat{j}+\hat{k}$ and $\overrightarrow{r}=5\hat{i}-6\hat{j}+6\hat{k}$? [Hint: linear velocity $\overrightarrow{v}=\overrightarrow{\omega }\times \overrightarrow{r}$]

An iron casting containing a number of cavities weighs $16000\text{N}$ in air and $12000\text{N}$ in water. Volume of the cavities in the casting is -
[ take density of iron $=8000{\text{kg/m}}^3$ & $g=10{\text{m/s}}^2$]

A block of mass $2\text{kg}$ attached to $3$ springs as shown in figure.





What is the angular frequency of oscillation if mass $m$ is slightly displaced from its equilibrium position ?

$(\text{Take,}k=100\text{N/m})$

If $y=x^3+2x^2+7x+8$, then $\frac{dy}{dx}$ will be

What is the speed of a projectile at a point on its path where it makes an angle of ${45}^{\circ }$ with the horizontal? It is given that the radius of curvature ($R$) of particle at this point is $50\sqrt{2}\text{m}$. Take $g=10{\text{m/s}}^2$.

7. What is a rigid body?

Two polaroids $P_1\text{and}{P}_2$ are placed with their axis perpendicular to each other. Unpolarised light $I_0$ is incident on $P_1.$ A third polaroid $P_3$ is kept in between $P_1\text{and}{P}_2$ such that its axis makes an angle ${45}^{\circ }$ with that of $P_1.$ The intensity of transmitted light through $P_2$ is

A parallel beam of light is incident from air at an angle $\alpha$ on the side PQ of a right-angled triangular prism of refractive index $n=\sqrt{2}$. Light undergoes total internal reflection in the prism at the face $PR$ when $\alpha$ has minimum value of ${45}^{\circ }$. The angle $\theta$ of the prism is

Two balls of masses $m_1=1\text{kg}$ and $m_2=2\text{kg}$ are attached to a massless rod of length $(l=1\text{m})$. Two parallel forces having equal magnitude of $F=1\text{N}$, opposite in direction (couple) are acting on both the balls as shown in the figure. Find the angular acceleration of the system ($\alpha$) about an axis passing through mid-point of the rod and also perpendicular to the plane of the rod. (Take anti-clockwise rotation as +ve)

In fig., $AB$ is a potentiometer wire of length $10\text{m}$ and resistance $2\Omega$. With key $\left(K\right)$ open the balancing length is $5.5\text{m}$. However, on closing key $\left(K\right)$ the balancing length reduces to $5\text{m}$. The internal resistance of the cell $\left(E_1\right)$ is –

In a Lloyd's single mirror experiment, the distance between the slit source and its image is $5mm$. The screen is at a distance of $1\text{m}$ from the source. The fringe width is observed to be $0.1mm$. Then the wavelength of light used is

Two capacitors of capacities $2C$ and $C$ are joined in parallel and charged up to potential $V$. The battery is removed and the capacitor of capacity $C$ is filled completely with a medium of dielectric constant $K$. The potential difference across the capacitors will now be :

A coil having N turns is wound tightly in the form of a spiral with inner and outer radii a and b respectively. When a current I passes through the coil, the magnetic field at the centre is

Pure inductors each of inductance $3\text{H}$ are connected as shown. The equivalent inductance of the circuit is