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Speeds of two identical cars are $u$ and $4u$ at a specific instant. If the same deceleration is applied on both the cars, the ratio of the respective distances in which the two cars are stopped from that instant is

The speed of longitudinal wave is given by $v=\sqrt{\frac{E}{\rho }}$ where $\rho$ is the density of the medium. Match the following columns for the quantities represented by $E$ in different media.
$\begin{array}{cccc}& \text{Column I}& & \text{Column II}\\ \text{(A)}& \text{Solid}& \text{(p)}& \text{Bulk modulus}\\ \text{(B)}& \text{Liquid}& \text{(q)}& \text{Shear modulus}\\ \text{(C)}& \text{Gas}& \text{(r)}& \text{Young's modulus}\end{array}$

Two uniform rectangular plates having mass density ($\text{mass/area}$) $2{\text{kg/m}}^2$ and $1{\text{kg/m}}^2$ are joined together to form the $\text{L}$- shaped lamina as shown in the figure. Find the coordinates of centre of mass of the $\text{L}$-shaped lamina.

The approximate depth of an ocean is $2700\text{m}$. The compressibility of water is $50\times {10}^{-11}{\text{Pa}}^{-1}$ and density of water is ${10}^3{\text{kg/m}}^3$. What fractional compression of water will be obtained at the bottom of the ocean?

A particle starts from the point $(0,8)m$ and moves with uniform velocity of $3\hat{i}$$m/sec$. After $5sec$, the angular velocity of the particle about the origin will be

A metal rod of $30\text{cm}$ length expands by $0.075\text{cm}$ when its temperature is raised from $0^{\circ }\text{C}$ to ${100}^{\circ }\text{C}$. Another rod of different metal of length $45\text{cm}$ expands by $0.045\text{cm}$ for the same rise in temperature. A composite rod $C$ made by joining $A$ and $B$ end to end expands by $0.040\text{cm}$ when its length is $45\text{cm}$ and it is heated from $0^{\circ }\text{C}$ to ${50}^{\circ }\text{C}$. Find the length of each portion of the composite rod.

The electric field in a region is radially outward with magnitude $E=A{\gamma }_0$ . The charge contained in a sphere of radius ${\gamma }_0$ centered at the origin is

A point source causes photoelectric effect from a small metal plate. Which of the following curves may represent the saturation photocurrent as a function of the distance between the source and the metal?

An ideal gas is expanding such that $P{T}^2=\text{constant}$. The coefficient of volumetric expansion of the gas is

If 5000 kg rocket is set for vertical firing the exhaust speed is 800 M per second to give an upward acceleration of 20 m per second squresthe amount of gas ejected per second to supply the needed thrust

What happens to the brightness of the lamps connected in series and parallel? Give reason.

Can we give as much charge as we wish to a capacitor??

The pressure at the same level in a water tank is:

Does the charging by friction violates law of conservation of charge?

A cylinder of given mass and density is constructed tht it's moment of inertia about an axis passing through its com and perpendicular to it's length is the minimum. If the length of the cylinder is root 6. Find radius

Why is the electric dipole from negative to positive charge?

The cover of a jar has diameter of 8 cm. 2 equal but opposite force of 20 N acts parallel to the rim of lid to turn it. What is the magnitude of the applied torque?

When a ball is thrown vertically upwards with velocity $v_0$, it reaches a maximum height of $h$. If one wishes to triple the maximum height then the ball should be thrown with velocity.

A small metallic sphere of mass $m$ is suspended from the ceiling of a car accelerating on a horizontal road with constant acceleration $a$ as shown in the figure. The tension in the string attached with the metallic sphere is

Seven capacitors each of capacity 2μFare to be so connected to have a total

capacity 10/11 μF. Which will be the necessary figure as shown

Assume that the total surface area of a human body is 1.6 $m^2$ and that it radiates like an ideal radiator. Calculate the amount of enrgy radiated per second by the body if the body temperature is ${37}^0$ C. Stefan constant $\sigma$ is $6.0\times {10}^{-8}W{m}^{-2}{K}^{-4}$ .

A bus starts to move with acceleration 1m/s^2. A man who is 48 m behind the bus runs to catch it with a constant velocity of 10 m/sec. In how much time he will catch the bus?

Monochromatic light of frequency ${\nu }_1$ irradiates a photocell and the stopping potential is found to be $V_1$. What is the new stopping potential of the cell if it is irradiated by monochromatic light of frequency ${\nu }_2$?

A beam of monochromatic blue light of wavelength $4200A^{\circ }$ in air travels in water $\mu =\frac{4}{3}$. Its wavelength in water will be

A satellite which is geostationary in a particular orbit is taken to another orbit. Its distance from the centre of earth in new orbit is 2 times that of the earlier orbit. The time period in the second orbit is

A cubical wooden box of side $L$ is placed on a horizontal rough surface and the coefficient of static friction between them is $\mu$. Another cubical box of same wood but of length $2L$ is placed on the same surface. Then the coefficient of static friction is

A uniform cylinder of mass $m$ and radius $R$ rolls without slipping down a slope of angle $\theta$ with the horizontal. The cylinder is connected to a spring having spring constant $K$ while the other end of the spring is connected to a rigid support at $P$. The cylinder is released when the spring is unstretched. The maximum distance that the cylinder travel along the plane is

A particle moves along a semicircle of radius 10 m in 5 seconds. The average velocity of the particle is

The mass of liquid flowing per second per unit area of cross section of the tube is proportional to $P^x$ and $v^y$, where $P$ is the pressure difference and $v$ is the velocity, then the relation between $x$ and $y$ is

A uniform rod of mass m and length l is struck at an end by a force F perpendicular to the rod for a short time interval t.

Calculate

(a) the speed of the centre of mass,

(b) the angular speed of the rod about the centre of mass,

(c) the kinetic energy of the rod and

(d) the angular momentum of the rod about the centre of mass after the force has stopped to act. Assume that t is so small that the rod does not appreciably change its direction while the force acts.

Radioactive tracer, or radioactive label are extensively used:

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An unloaded bus can be stopped by applying brakes on straight road after covering a distance x. Suppose the passanger adds 50% of its weight as the load and the braking force remains the same how far will the bus go after the application of the brakes ? (Velocity of the bus in both case is same)

A child stands at the centre of a turntable with his two arms outstretched. The turntable is set rotating with an angular speed of 40 rev/min. How much is the angular speed of the child if he folds his hands back and thereby reduces his moment of inertia to 2/5 times the initial value? Assume that the turntable rotates without friction.
Show that the child’s new kinetic energy of rotation is more than the initial kinetic energy of rotation. How do you account for this increase in kinetic energy?

What is the coefficient of thermal conductivity K?

Which of the following equation holds true for linear momentum (p) of a system of i particles with masses m₁, m₂, ..........m_i, moving with velocities v₁, v_2,............... v_i.

A particle moves along the x-axis. Its velocity time-graph is given below.

The particle changes its direction of acceleration, when

Two masses $m_1$ and $m_2$ are moving with velocities $v_1$ and $v_2$ respectively. Find their total kinetic energy in the reference frame of centre of mass.