Mechanics PYQ — Page 5

If a soap bubble expands, the pressure inside the bubble

A body of mass $60g$ experiences a gravitational force of $3.0N$, when placed at a particular point. The magnitude of the gravitational field intensity at that point is

Plane angle and solid angle have:

A spherical ball is dropped in a long column of a highly viscous liquid. The curve in the graph shown, which represents the speed of the ball $(v)$ as a function of time $(t)$ is 

The terminal velocity of a copper ball of radius $5 \mathrm{~mm}$ falling through a tank of oil at room temperature is $10 \mathrm{~cm} \mathrm{~s}^{-1}$. If the viscosity of oil at room temperature is $0.9 \mathrm{~kg} \mathrm{~m}^{-1} \mathrm{~s}^{-1}$, the viscous drag force is:

In the diagram shown, the normal reaction force between $2 \mathrm{~kg}$ and $1 \mathrm{~kg}$ is (Given $g=10 \mathrm{~ms}^{-2}$) (Consider the surface, to be smooth): 

The area of a rectangular field (in ${m}^{2}$) of length $55.3m$ and breadth $25m$ after rounding off the value for correct significant digits is:

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R), Assertion (A): When a fire cracker (rocket) explodes in mid air, its fragments fly in such a way that they continue moving in the same path, which the fire cracker would have followed, had it not exploded Reason (R): Explosion of cracker (rocket) occurs due to internal forces only and no external force acts for this explosion. In the light of the above statements, choose the most appropriate answer from the options given below:

The dimensions $[\mathrm{MLT}{A-2}^{-2}]$ belong to the

Given below are two statements : One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): The stretching of a spring is determined by the shear modulus of the material of the spring. Reason (R): A coil spring of copper has more tensile strength than a steel spring of same dimensions. In the light of the above statements, choose the most appropriate answer from the options given below :

Two copper vessels $A$ and $B$ have the same base area but of different shapes. A takes twice the volume of water as that $B$ requires to fill upto a particular common height. Then the correct statement among the following is:

A shell of mass $m$ is at rest initially. It explodes into three fragments having mass in the ratio $2:2:1$. If the fragments having equal mass fly off along mutually perpendicular directions with speed $v$, the speed of the third (lighter) fragment is:

The displacement-time graphs of two moving particles make angles of $30^{\circ}$ and $45^{\circ}$ with the $x$-axis as shown in the figure. The ratio of their respective velocity is: 

An electric lift with a maximum load of $2000\mathrm{kg}$ (lift $+$ passengers) is moving up with a constant speed of $1.5{ms}^{-1}$. The frictional force opposing the motion is $3000N$. The minimum power delivered by the motor to the lift in watts is : $(g=10{ms}^{-2})$

The energy that will be ideally radiated by a $100\mathrm{kW}$ transmitter in $1$ hour is

The ratio of the distances travelled by a freely falling body in the ${1}^{\mathrm{st}},{2}^{\mathrm{nd}},{3}^{\mathrm{rd}}$ and ${4}^{\mathrm{th}}$ second

A small block slides down on a smooth inclined plane, starting from rest at time $t=0$. Let ${S}_{n}$ be the distance travelled by the block in the interval $t=n-1$ to $t=n$. Then, the ratio $\frac{{s}_{n}}{{s}_{n+1}}$ is:

A particle of mass $m$ is projected with a velocity $v=k{V}_{e}(k<1)$ from the surface of the earth (${V}_{e}=$ escape velocity). The maximum height above the surface reached by the particle is___

A ball of mass $0.15\mathrm{kg}$ is dropped from a height $10m$ strikes the ground and rebounds to the same height. The magnitude of impulse imparted to the ball is $(g=10m{s}^{-2})$ nearly :

Water falls from a height of $60m$ at the rate of $15\mathrm{kg}{s}^{-1}$ to operate a turbine. The losses due to frictional force are $10%$ of the input energy. How much power is generated by the turbine? $(g=10m{s}^{-2})$

A particle is released from height $S$ from the surface of the Earth. At a certain height its kinetic energy is three times its potential energy. The height from the surface of the earth and the speed of the particle at that instant are respectively___

A screw gauge gives the following readings when used to measure the diameter of a wire Main scale reading : $0\mathrm{mm}$ Circular scale reading : $52\mathrm{divisions}$ Given that $1\mathrm{mm}$ on main scale corresponds to $100\mathrm{divisions}$ on the circular scale. The diameter of the wire from the above data is:

A particle moving in a circle of radius $R$ with a uniform speed takes a time $T$ to complete one revolution. If this particle were projected with the same speed at an angle $\theta$ to the horizontal, the maximum height attained by it equals $4R$. The angle of projection $\theta$ is then given by___

A car starts from rest and accelerates at $5m{s}^{-2},\text{at}t=4s$, a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at $t=6s$ ? $(g=10m{s}^{-2})$