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Two plates of 8 mm thickness each are connected by a fillet weld of 6 mm thickness as shown in figure below.







The permissible stresses in the plate and the weld are 160 MPa and 120 MPa, respectively. Assuming the length of the weld as shown in the figure to be the effective length, the permissible tensile load P is kN.

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A solid sphere of mass 2 kg is resting inside a cube as shown in the figure. The cube is moving with a velocity $v=(5t\hat{i}+2t\hat{j})m/s$.Here t is the time in second. All surface are smooth. The sphere is at rest with respect to the cube. What is the total force exerted by the sphere on the cube. (Take $g=10m/s^2).$

A ray is incident at an angle of incidence $i$ on one surface of a small angled prism (with angle of prism $8^{\circ })$ and emerges normally from the opposite surface. If the refractive index of the material of prism is $\frac{3}{2},$ then the angle of incidence is nearly equal to

Ratio of moment of inertia, $I_1:I_2$ of a uniform square plate about shown axes is

The coefficient of friction between the tyres and the road is 0.25. The maximum speed with which a car can be driven round a curve of radius 40 m without skidding is $(assumeg=10m{s}^{-2})$

.What are the values of pressure, temperature, and molar volume at stp and ntp

A body of mass 0.5 kg is projected under gravity with a speed of 98 m/s at an angle of ${30}^{\circ }$ with the horizontal. The change in momentum (in magnitude) of the body is

A heavy particle hangs from a point O, by a string of length a. It is projected horizontally with a velocity $v=\sqrt{(2+\sqrt{3})ag}$.

The angle with the upward vertical, string makes where string becomes slack is

An electron moves along the line PQ which lies in the same plane as a circular loop of conducting wire, as shown in Fig. 25.5. What will be the direction of the induced current, if any, in the loop?

Two identical thin plano-convex glass lenses of refractive index $1.50$ each having radius of curvature of $20\text{cm}$ are placed with their convex surfaces in contact at the centre. The intervening space is filled with the liquid of refractive index $1.7$ as shown in figure. The focal length of this combination is

The turn ratio of a transformers is given as 2 : 3. If the current through the primary coil is 3 A, thus calculate the current through load resistance

A rod $PQ$ of length $L$ moves with a uniform velocity $v$ parallel to a long straight wire carrying a current $i$. The end $P$ of the rod always remains at a distance $r$ from the wire. Calculate the emf induced across the rod.



Take, $v=5.0\text{m/s},i=100\text{A},r=1.0\text{cm}$ and $L=19\text{cm},{\log }_{e}20=3$

Consider an expanding sphere of instantaneous radius $R$ whose total mass remains constant. The expansion is such that the instantaneous density $\rho$ remains uniform throughout the volume. The rate of fractional change in density $\left(\frac{1}{\rho }\frac{d\rho }{dt}\right)$ is constant. The velocity $v$ of any point on the surface of the expanding sphere is proportional to

If $y={\sin }^5\theta +{\cos }^8\theta$. Find $\frac{dy}{d\theta }$.

Light of
wavelength 488 nm is produced by an argon laser which is used in the
photoelectric effect. When light from this spectral line is incident
on the emitter, the stopping (cut-off) potential of photoelectrons is
0.38 V. Find the work function of the material from which the emitter
is made.

Based on the given graph between electric field $\left(E\right)$ and distance $\left(r\right)$ from axis of the infinite uniformly charged solid non-conducting cylinder, the charge density is

[$R$ is radius of cylinder]

The coil of an a.c generator rotates at a frequency of $60\text{Hz}$ and develops an induced emf of $120\text{V}$(rms). Area of the coil is $3\times {10}^{-3}{\text{m}}^2$ and number of turns is $N=500.$ The magnitude of magnetic field in which the coil rotates is

A cylindrical vessel with a cross sectional area $A$ has a small hole of area $a$ at the bottom. A liquid is filled in the vessel upto a height $H$. Find the time taken to empty the tank.

Two swimmers swim in a stand still lake. First swimmer swims directly across the lake ($30m$ wide) with a velocity of $1.5m/s$, reaches the other end and runs a distance of $10m$ in $10$ seconds along the shore. What should be the velocity of the second swimmer so that he reaches the same point in the same time ?

A particle is projected at angle θ with horizontal with velocity $V_0$

Find

(i) tangential and normal acceleration of the particle at t = 0 and at highest point of its trajectory.

(ii) radius of curvature at t = 0 and highest point.

In order to measure temperature across a tank $Cu-Cn\left(10\mu V{/}^{\circ }C\right)$ and $In-Cn\left(20\mu V{/}^{\circ }C\right)$ are attached alternatively as shown below. A Voltmeter is attached to measure the voltage. The reading of the Voltmeter is

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Current move opposite to the direction of electrons ,then how scientists came to about electricity even before electrons were discovered

An insulated wire is wound so that it forms a flat coil with $N$ turns. The radii of the inner and outermost turns are $r_1$ and $r_2$ respectively. What will be the magnetic moment of this coil when a current $I$ flows through it ?

A point source is placed at a depth h below the surface of water (refractive index $=\mu$).

(a) Show that light escapes through a circular area on the water surface with its centre directly above the point source.

(b) Find the angle subtended by a radius of the area on the source.

A particle starts moving rectilinearly at time t = 0 such that its velocity ‘v’ changes with time ‘t’ according to the equation $v=t^2-t$ where t is in seconds and v in m/s. Find the time interval for which the particle retards.

Two cars moving in opposite directions approach each other with speeds of $40{\text{ms}}^{-1}$ and $50{\text{ms}}^{-1}$ respectively. The driver of the first car blows a horn of frequency $400\text{Hz}$. The frequency heard by the driver of the second car is

[speed of sound $=340{\text{ms}}^{-1}$]

A bar magnet is demagnetised by inserting it inside a solenoid of length $0.2\text{m}$ having $100$ turns and carrying a current of $5.2\text{A}.$ The coercivity of the bar magnet is-

A constantly moving positively charged particle is spotted at point $(5\text{cm},0,0)$ at a given instant. At the same instant magnetic field produced by it at origin is detected to be $\overrightarrow{B}=B_0\hat{j}$; where $B_0$ is a positive constant. The possible instantaneous velocity of the charged particle is :

A body starts from rest with a uniform acceleration. If its velocity after $n$ second is $v$, then its displacement in the last $2\text{s}$ is