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A lorry and a car moving with the same momentum are brought to rest by the application of brake, which provide equal retarding force? Which of them will come to rest in shorter time? Which will come to rest in less distance?

The number of electrons ,protons and neutrons in a species are equal to 18, 16 and 16 respectively. Assign the proper symbol to the species.

Find the energy, the frequency and the momentum of an X-ray photon of wavelength 0.10 nm.

A double convex thin lens made of glass of refractive index 1.6 has radii of curvature 15 cm each. The focal length of this lens when immersed in a fluid of refractive index 1.63 is

Object $A$ of mass $m$, is moving at a velocity $v_1$ to the right. It collides and sticks to object $B$ of mass $m_2$ moving in the same direction as object $A$ with velocity $v_2$. After collision, both the objects have the same velocity $\frac{1}{2}(v_1+v_2)$. What is the relationship between $m_1$ and $m_2$? [$v_1$ and $v_2$ are not equal]

The field normal to the plane of a wire of n turns and radius r which carries a current i is measured on the axis of the coil at a small distance h from the centre of the coil. This is smaller than the field at the centre by the fraction of

A spherical shell is cut into two pieces along a chord and separated by a large distance as shown in figure. For points $A$ and $B$, where $V$ and $\overrightarrow{E}$ are gravitational potential and field respectively, then

Paragraph : When the rays of light after being incident on a mirror, get reflected, two situations are possible. The rays may either intersect actually or they may diverge; in which case if extrapolated they appear to intersect. A real image is formed in the former case and a real image in the later.

Q If converging incident rays fall on a convex mirror:

A block of mass 25 kg is raised by a 50 kg man in two different ways as shown in Fig.5.19. What is the action on the floor by the man in the two cases? If the floor yields to a normal force of 700 N, which mode should the man adopt to lift the block without the floor yielding?

The equation of a stationary wave is y = 0.8 cos $\left(\frac{\pi x}{20}\right)sin200\pi t$ , where x is in

cm and t is in sec. The separation between consecutive nodes will be

[MP PET 1994]

Refractive index for a material for infrared light is

[CPMT 1984]

The equilibrium constant for a reaction is 10. $\Delta G^{\circ }$ will be:
$\left(\text{R= 8 J/Kmol, T = 300 K}\right)$

Find the tension in the inextensible string using pseudo-force concept. (Take $g=10m/s^2$)

A ball weighing 0.01kg hits a hard surface vertically with a speed of 5m/s and rebounds with the same speed. The ball remains in contact with the surface for 0.01s. The average force exerted by the surface on the ball is

A body is projected up a smooth inclined plane (length = $20\sqrt{2}m$ ) with velocity u from the point M as shown in the figure. The angle of inclination is ${45}^{\circ }$ and the top is connected to a well of diameter 40 m. If the body just manages to cross the well, what is the value of v

A block of mass 20 kg moving at 2.0 m/s collides head on with another block of equal mass at rest. The maximum possible loss in kinetic energy due to the collision is:

A hockey punk with a mass of 0.3 kg slides on the horizontal frictionless surface of an ice rink. Two forces act on the punk as shown in figure. The force F1 has a magnitude of 5N and F2 has a magnitude of 8N.Determine the acceleration of the punk

If p and q are the lengths of perpendiculars from the origin to the lines $xcos\theta –ysin\theta =3cos2\theta$ and $xsec\theta +ycosec\theta =3$, respectively, then the value of $p^2+4q^2$ is

An ideal spring with spring-constant k is hung from the ceiling and a block of mass M is attached to its lower end. The mass is released suddenly with the spring initially unstretched. Then the maximum extension in the spring is

A boy of mass $60\text{kg}$. He wants to swim in a river with the help of a wooden log. If relative density of wood is $0.6$, what is the minimum volume of wooden log?
(density of river water is $1000{\text{kg/m}}^3$)

Calculate the phase difference between voltage and current, when R = 200 Ohms, L = 1

H,. v = 200/2πHz

A radioactive nucleus is being produced at a constant rate α per second. Its decay constant is λ If N0are the
number of nuclei at time t = 0, then maximum number of nuclei possible are

$Ify=\frac{(x^2+2x)}{(3x-4)},then\frac{dy}{dx}=?$

Ratio of rotational kinetic energy to the total energy for diatomic gas molecule at room temperature is

If $\text{tan}{\theta }_1.\text{tan}{\theta }_2=-\frac{a^2}{b^2}$ then the chord joining two points ${\theta }_1$ and ${\theta }_2$ on the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ will subtend a right angle at:

Two cars $A$ and $B$ are travelling in the same direction with velocities $v_1$ and $v_2(v_1>v_2)$ respectively. When the car $B$ is at a distance $d$ ahead of the car $A$, the driver of the car $A$ applied the brake producing a uniform retardation $a$. There will be no collision if

If a vector $\hat{i}+x\hat{j}$ is rotated through an angle $\theta$ and its magnitude is doubled, then it becomes $\hat{i}+4x\hat{j}$. The value of $x$ may be

A block of mass m compresses a spring of stiffness k through a distance l/2 as shown in the figure. If the block is not fixed to the spring and released from this position, the period of motion of the block is

Dimensional formula of electric field

The angle between vector $\overrightarrow{A}$ and $-2\overrightarrow{A}$ is

A right-angled prism of apex angle $4^{\circ }$ and refractive index $1.5$ is located in front of a vertical plane mirror as shown in figure. A horizontal ray of light is falling on the prism. Find the total deviation produced in the light ray as it emerges 2nd time from the prism.

A particle is dropped from the tower. The distance travelled by it in the last second is $15\text{m}$. The height of the tower is
[Take $g=10{\text{m/s}}^2$]

What is back emf

Due to some force $F_1$ a body oscillates with period 4/5 sec and due to other force $F_2$ oscillates with period 3/5 sec. If both forces act simultaneously, the new period will be

One end of a uniform wire of length $L$ and of weight $W$ is attached rigidly to a point in the ceiling and a weight $W_1$ is suspended from its lower end. If $S$ is the area of cross–section of the wire, the stress in the wire at a height $3L/4$ from its lower end is

A $0.2\text{kg}$ object at rest is subjected to a force $(0.3\hat{i}-0.4\hat{j})\text{N}$. What is the velocity of the object (in $m/s$) after $6\text{s}$

The blocks $B$ and $C$ in the figure have mass $m$ each. The strings $AB$ and $BC$ are light, having tensions $T_1$ and $T_2$ respectively. The system is in equilibrium with a constant horizontal force $mg$ acting on $C$. Then

A block of mass m is kept over another block of mass M and the system rests on a horizontal surface (figure 8-E1). A constant horizontal force F acting on the lower block produces an acceleration $\frac{F}{2(m+M)}$ in the system, the two blocks always move together. (a) Find the coefficient of kinetic friction between the bigger block and the horizontal surface. (b) Find the frictional force acting on the force of friction on the smaller block by the bigger block during a displacement d of the system.

A rod of length 4m is rotated about an axis perpendicular to the rod and passing through a point 1 m from one of its end as shown in figure. The rod has a uniform mass density and has a total mass of 10 kg. What will be its moment of Inertia about this axis?

A copper cube of mass 200 g slides down on a rough inclined plane of inclination ${37}^0$ at a constant speed. Assume that any loss in mechanical energy goes into the copper block as thermal energy. Find the increase in the temperature of the block as it slides down through 60 cm. Specific heat capacity of copper = 420 J $k{g}^{-1}{K}^{-1}$.

A point source of light B is placed at a distance 'L' in front of the center of a mirror of width 'd' hung vertically on a wall. A man walks in front of the mirror along a line parallel to the mirror at a distance '2L' from it as shown in the figure. The greatest distance over which he can see the image of the light source in the mirror is

Two soap bubbles of radii $4\text{cm}$ and $5\text{cm}$ are touching each other over a common surface $S_1{S}_2$ (shown in figure). Then, radius of the common surface will be

If the radius of curvature of the path of two particles having same speed are in the ratio of $1:\sqrt{2}$, then in order to have masses in the ratio of $2:1$, their centripetal forces should be in the ratio of