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A bar magnet of moment $\overrightarrow{M}=\hat{i}+\hat{j}$ is placed in a magnetic field induction $\overrightarrow{B}=3\hat{i}+4\hat{j}+4\hat{k}$. The torque acting on the magnet is-

A block of mass 250 g slides down an incline of inclination ${37}^{\circ }$ with a uniform speed. Find the work done against the friction as the block slides through 1.0 m.

A uniform wooden stick of mass 1.6 kg of length $l$ rests in an inclined manner on a smooth, vertical wall of height $h(<l)$ such that a small portion of the stick extends beyond the wall. The reaction force of the wall on the stick is perpendicular to the stick. The stick makes an angle of ${30}^{\circ }$ with the wall and the bottom of the stick is on a rough floor. The ratio $\frac{h}{l}$ and the frictional force $f$ at the bottom of the stick are $(g=10m{s}^{-2})$. Also, the normal reactions at the two points of contact on the stick are equal.

Potential energy for a conservative force $\overrightarrow{F}$ is given by $U(x,y)=\cos (x+y)$. Force acting on a particle at position given by coordinates $(0,\frac{\pi }{4})$ is

A block weighing 10 N travels down a smooth curved track AB joined to a rough horizontal surface (figure 8-E5). The rough surface has a friction coefficient of e20 with the block. If the block starts slipping on the track from a point 1'0 in above the horizontal surface,how far will it move on the rough surface ?

What will be the final linear momentum of an electron, when it is accelerated through a potential difference of $100\text{V}$, if it is initially at rest?

A
toroid has a core (non-ferromagnetic) of inner radius 25 cm and outer
radius 26 cm, around which 3500 turns of a wire are wound. If the
current in the wire is 11 A, what is the magnetic field (a) outside
the toroid, (b) inside the core of the toroid, and (c) in the empty
space surrounded by the toroid.

A person traveling at 43.2 km/h applies the brake giving a deceleration of 6.0 m/$s^2$ to his scooter. How far will it travel before stopping?

In thermal equilibrium, the average velocity of gas molecules is

A $0.098\text{kg}$ block slides down a frictionless track as shown (Assume no energy loss on the entire track)

The vertical component of the velocity of block at $A$ is

How do woollen clothes keep us warm?

A box is placed on an inclined plane and has to be pushed down. The angle of inclination is

The equation of projectile is $y=16x-\frac{5x^2}{4}$ . The horizontal range is

Light strikes a sodium surface, causing photoelectric emission. The stopping potential for the ejected electrons is 5.0 V, and the work function of sodium is 2.2 eV. What is the wavelength of the incident light? __nm.

A transparent thin film of uniform thickness and refractive index $n_1=1.4$ is coated on the convex spherical surface of radius R at one of a long solid glass cylinder of refractive index $n_2=1.5,$ as shown in the figure. Rays of light parallel to the axis of the cylinder traversing through the film from air to glass get focused at a distance $f_1$ from the film, while rays of light traversing from glass to air get focused at a distance $f_2$ from the film. Then

Figure shows a smooth track, a part of which is a circle of radius $r$. A block of mass $m$ is pushed against a spring of spring constant $k$ fixed at the left end and is then released. Find the initial compression of the spring so that the block presses the track with a force $mg$ when it reaches the point $P$, where the radius of the track is horizontal.

Consider a sphere of radius $R$, which carries a uniform charge density $\rho$. If a sphere of radius $\frac{R}{2}$ is carved out of it, as shown, the ratio $\frac{\left|{\overrightarrow{E}}_A\right|}{\left|{\overrightarrow{E}}_B\right|}$ of the magnitudes of electric field $\overrightarrow{E_A}\text{and}\overrightarrow{E_B}$, respectively, at points $A$ and $B$, due to the remaining portions is:

1. 1.75

Energy generation in stars is mainly due to

From rest you suddenly stand up and start walking. But according to Newton's first law there has to be a force for change of state. What force made you move?

A thin rectangular magnet suspended freely has a period of oscillation equal to $T$. Now it is broken into two equal halves (each having half of the original length) and one piece is made to oscillate freely in the same field. If its period of oscillation is $T^{\prime }$, the ratio $\frac{T^{\prime }}{T}$ is

A particle of charge per unit mass $\alpha$ is projected from origin with a velocity $\overrightarrow{v}=v_0\hat{i}$ in a uniform magnetic field $\overrightarrow{B}=-B_0\hat{k}$. If the particle passes through $(0,y,0)$ then $y$ is equal to

How do observations figure in the scientific method?

The reflection of the parallel rays of a torch light can be seen by only one observer. Why? [3 MARKS]

A ball thrown by a boy is caught by another after 2 sec. some distance away in the same level. If the angle of projection is ${30}^{\circ }$, the velocity of projection is

A coil has negligible resistance and an inductive reactance of $20\Omega$ at $50\text{Hz}$. If an AC source of $200\text{V}$ and $100\text{Hz}$ frequency is connected across the coil, the rms current in the coil will be

1. 1800