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The motion of a body is given by the equation $\frac{dv\left(t\right)}{dt}=6.0-3v\left(t\right)$. where v(t) is speed in m/s and t in sec. If body was at rest at t=0

What is the difference between tension and surface tension?

Water in subcritical flows in a horizontal frictionless channel experiences steep drops in bed. What is/are the possible type of GVF profile?

1. -70.7

The radius vector describing the position of the particle $A$ relative to origin is $\overrightarrow{r}=t^2\hat{i}+(t-1{)}^2\hat{j}$.
Find the rectangular components of the average velocity in the time interval between $t$ and $t+\Delta t$ ?

A cylinder is released from rest from the top of an inclined plane of inclination $\theta$ and length 'l'. If the cylinder rolls without slipping, what will be its speed when it reaches the bottom?

Three boys are standing on a horizontal paltform of mass $170\text{kg}$ and length $6\text{m}$ is as shown in figure. They exchange their position as shown in the figure. Distance moved by the platform is : (Neglect friction)

Find the flux of the electric field through surface $\text{ABCD}$ of the inclined plane as shown in figure.

The height y and distance x along the horizontal plane of a projectile on a certain planet are given $y=8t-5t^2\left(mtr\right)$ and $x=6t\left(mtr\right)$. The acceleration due to gravity is:

A neutron moving at a speed 'v' undergoes a head-on elastic collision with a nucleus of mass number 'A' at rest. The ratio of the kinetic energies of the neutron after and before collision is

Two resistances $R_1$ and $R_2$ are joined as shown in the figure to two batteries of e.m.f. $E_1$and $E_2$. If $E_2$is short-circuited, the current through $R_1$ is

A solid sphere of mass $1\text{kg}$ and radius $2\text{m}$ slips on a rough horizontal plane. At some instant, it has translational velocity $7\text{m/s}$ and angular velocity $\frac{7}{4}\text{rad/s}$ about its centre. The translational velocity after the sphere starts pure rolling is

A stone is thrown up towards a mango, it hits the mango and the stone falls down. Identify the graph of the motion of the stone.

When a glass prism of refracting angle ${60}^{\circ }$ is immersed in a liquid, its angle of minimum deviation is ${30}^{\circ }$. The critical angle of glass with respect to the liquid medium is

Determine the escape velocity of a rocket on the far side of a moon of a planet. The radius of the moon is $2.64\times {10}^6$m and its mass is $1.495\times {10}^{23}$. The mass of the planet is $1.9\times {10}^{27}$kg, and the distance between planet and the moon is $1.071\times {10}^9$m. Include the gravitational effect of planet and neglect the motion of the planet and the moon as they rotate about their CM.

The instantaneous values of alternating current and voltages in a circuit are given as

$I=\frac{1}{\sqrt{2}}\sin \left(100\pi t\right)\text{A}$

$V=\frac{1}{\sqrt{2}}\sin (100\pi t+\frac{\pi }{3})\text{V}$

The average power (in watts) consumed in the circuit is

Moment of Inertia $\left(MI\right)$ of four bodies, having same mass and radius, are reported as -



$I_1=MI$ of thin circular ring about its diameter.



$I_2=MI$ of circular disc about an axis perpendicular to the disc and passing through the centre.



$I_3=MI$ of solid cylinder about its axis.



$I_4=MI$ of solid sphere about its diameter.



Then :

The value of $\int \frac{dx}{(3\sin x-4\cos x{)}^2}$ is

(where $C$ is integration constant)

The factor not needed to calculate heat lost or gained when there is no change of state is:

Consider a solid cylinder of density ${\rho }_s$ cross – sectional area A and height h floating in a liquid of density ${\rho }_l$, as shown in the adjacent figure $({\rho }_l>{\rho }_s)$. It is depressed slightly and allowed to oscillate vertically.

The frequency of small oscillations is

A mass $\text{M}$ is lowered with the help of a string by a distance $\text{x}$ at a constant acceleration $\frac{g}{2}$. The magnitude of work done by the string will be