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If force, $F=120N$ is acting parallel to the inclined plane, find tension $T$ in the string as shown in the figure. All surfaces are smooth.
(Take $g=10{\text{m/s}}^2$).

A wire $\text{PQ}$ of mass $10\text{g}$ is at rest on two parallel metallic rails. The separation between the rails is $4.9\text{cm}$. A magnetic field of $0.80\text{T}$ is applied perpendicular to the plane of the rails, directed downwards. The resistance of the circuit is slowly decreased. When the resistance decreases to below $20$ $\Omega$, the wire $\text{PQ}$ begins to slide on the rails. Calculate the coefficient of friction between the wire and the rails.

An insect crawls up a hemispherical surface very slowly, figure. The coefficient of friction between the insect and the surface is $1/3$. If the line joining the center of the hemispherical surface to the insect makes an angle $\alpha$, the maximum possible value of $\alpha$ is given by

What is the moment of Inertia of a uniform hollow sphere of mass $M$ and radius $R$, about its diameter

An oscillator is nothing but an amplifier with

A unit vector parallel to the resultant of the vectors $\overrightarrow{A}=\hat{i}+4\hat{j}-2\hat{k}$ and $\overrightarrow{B}=3\hat{i}-5\hat{j}+\hat{k}$ is

Figure (10 - E14) shows a rough track, a portion of which is in the form of a cylinder of radius R. With what minimum linear speed should a sphere of radius r be set rolling on the horizontal part so that it completely goes round the circle on the cylindrical part.

A table with a smooth horizonal surface is placed in a cabin which moves in a horizontal circle of a large radius $R$. A smooth pulley of small radius is fixed to the table. Two masses $m$ and $2m$ placed on the table are connected through a light string going over the pulley. System is released from rest with respect to the cabin. The initial tension in the string will be:

A stone falls freely from rest and the total distance covered by it in the last second of its motion equals the distance covered by it in the first three second of its motion. The stone remains in the air for

A concave lens forms the image of an object such that the distance between the object and image is $10\text{cm}$ and the magnification produced is $\frac{1}{4}$. The focal length of the lens will be

Two point mass $50\text{g}$ and $100\text{g}$ are attached to the ends of a rod of length $2\text{m}$ and of negligible mass. The rod which was initially at rest is set into rotation about an axis perpendicular to the length of the rod. Find the position of axis of rotation from $50\text{g}$ about which the work required to set the rod into rotation with an uniform angular velocity of $2\text{rad/s}$, is minimum.

In a glass slab of thickness ${}^{\prime }{l}^{\prime }$ and refractive index ${\mu }_1$, a cuboidal cavity of thickness 'm' is carved and filled with a liquid of refractive index ${\mu }_2({\mu }_1>{\mu }_2)$. It has been found that shift produced by the given slab is zero when an observer 'A' observes an object 'B', the ratio $l/m$ will be :

(consider the incident rays to be paraxial)

The angular speed of a fly wheel making 120 revolutions/minute is

Two protons exerts a nuclear force on each other, the distance between them is

For series $L-C-R$, graph between peak current and frequency ($\omega$) shown in the figure below.
The correct order for $R_1,R_{2}and{R}_3$

The position of the particle moving on $X$-axis is given by, $X=A{t}^3+B{t}^2+Ct+D.$ The numerical values of $A,B,C,D$ are $1,4,-2$ and $5$ respectively and SI units are used. Find the average velocity during the interval $t=0$ to $t=4s$.

A wagon weighing 1000 kg is moving with a velocity 50 km/h on smooth horizontal rails. A mass of 250 kg is dropped into it. The velocity with which it moves now is

All the inner angles of a - 7 sided polygon are obtuse, their sizes in degree being distinct integers divisible by 9. What is the sum (in degree) of the largest two angles?

Two blocks of masses $5\text{kg}$ and $2\text{kg}$ are connected by a massless string as shown in figure. A vertical force $F$ is applied on the $5\text{kg}$ block. Find the value of $F$ if tension in the string is $40\text{N}$. $(g=10{\text{m/s}}^2)$

Two masses $m$ and $2m$ are at rest initially. Find the velocity of mass $2m$, when their separation reduces to $\frac{d}{2}$ due to gravitational force of attraction.

A $200\text{Hz}$ wave with amplitude $1\text{mm}$ travels on a long string of linear mass density $6{\text{g m}}^{-1}$ kept under a tension of $60\text{N}$. The average power transmitted across a given point in the string is

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नीचे दिए गए प्रश्न के लिए अनुच्छेद



Velocities of end points of a uniform rod of mass M and length L is shown in figure. Then



M द्रव्यमान व L लम्बाई की एकसमान छड़ के सिरों के वेग चित्रानुसार हैं। तब





Q. Kinetic energy of rod is



प्रश्न - छड़ की गतिज ऊर्जा है

A proton moves at a speed of $v=2\times {10}^6\text{m/s}$ in a region of constant magnetic field of magnitude $0.05\text{T}$. The direction of the proton with the field is $\theta ={30}^{\circ }$ when it enters. When you look along the direction of the magnetic field, the path is a circle projected on a plane perpendicular to the magnetic field. How far will the proton moves along the direction of $B$, when two projected circles have bean completed ?

In a series $\text{LCR}$ circuit $L=1\text{H},C=6.25\mu \text{F}$ and $R=1\Omega$. Its quality factor is-

Blocks A and B are resting on a smooth horizontal surface given equal speeds of $2\text{m/s}$ in opposite sense as shown in the figure.



At $t=0$, the position of blocks are shown, then the co-ordinates of centre of mass at $t=3\text{s}$ will be

What is the order of ip2 values of boron and beryllium? Can we check it by using effective nuclear charge concept or is there any other procedure?

A wheel is rotating freely with an angular speed $\omega$ on a shaft. The moment of inertia of the wheel is $I$ and the moment ot inertia of the shaft is negligible. Another wheel of moment of inertia $3I$ initially at rest is suddenly coupled to the same shaft. The resultant fractional loss in the kinetic energy of the system is

A wire of length $L$, area of cross-section $A$ is hanging from a fixed support. The length of the wire changes to $L_1$ when mass $M$ is suspended from its free end. The expression for Young's modulus is :

Two rectangular blocks A and B of different metals have same length and same area of cross-section. They are kept in such a way that their cross-sectional area touch each other. The temperature at one end of A is ${100}^{o}C$ and that of B at the other end is $0^{o}C$. If the ratio of their thermal conductivity is 1 : 3, then under steady state, the temperature of the junction in contact will be