Mechanics PYQ — Page 17

A given object takes $\mathrm{n}$ times the time to slide down $45^{\circ}$ rough inclined plane as it takes the time to slide down an identical perfectly smooth $45^{\circ}$ inclined plane. The coefficient of kinetic friction between the object and the surface of inclined plane is :

A cube of ice floats partly in water and partly in kerosene oil. The ratio of volume of ice immersed in water to that in kerosene oil (specific gravity of Kerosene oil $=0.8$, specific gravity of ice $=0.9$) 

A wire of cross sectional area A, modulus of elasticity $2 \times 10^{11} \mathrm{Nm}^{-2}$ and length $2 \mathrm{~m}$ is stretched between two vertical rigid supports. When a mass of $2 \mathrm{~kg}$ is suspended at the middle it sags lower from its original position making angle $\theta=\frac{1}{100}$ radian on the points of support. The value of $\mathrm{A}$ is _______ $\times 10^{-4} \mathrm{~m}^2$ (consider $x< < \mathrm{L}$ ). (given : $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$ )

A cricket player catches a ball of mass $120g$ moving with $25m{s}^{-1}$ speed. If the catching process is completed in $0.1s$ then the magnitude of force exerted by the ball on the hand of player will be(in SI unit):

A clock has $75 \mathrm{~cm}, 60 \mathrm{~cm}$ long second hand and minute hand respectively. In 30 minutes duration the tip of second hand will travel $x$ distance more than the tip of minute hand. The value of $x$ in meter is nearly (Take $\pi=3.14$ ) :

The measured value of the length of a simple pendulum is $20\mathrm{cm}$ with $2\mathrm{mm}$ accuracy. The time for $50$ oscillations was measured to be $40$ seconds with $1$ second resolution. From these measurements, the accuracy in the measurement of acceleration due to gravity is $N%$. The value of $N$ is:

Applying the principle of homogeneity of dimensions, determine which one is correct, where $T$ is time period, $G$ is gravitational constant, $M$ is mass, $r$ is radius of orbit.

What is the range of the ball along the inclined plane?

Two blocks of mass $2\mathrm{kg}$ and $4\mathrm{kg}$ are connected by a metal wire going over a smooth pulley as shown in figure. The radius of wire is $4.0\times {10}^{-5}m$ and Young's modulus of the metal is $2.0\times {10}^{11}N{m}^{-2}$. The longitudinal strain developed in the wire is $\frac{1}{\alpha \pi }$. The value of $\alpha$ is _____. [Use $g=10m{s}^{-2}$) 

The angle of projection for a projectile to have same horizontal range and maximum height is :

A body falling under gravity covers two points $A$ and $B$ separated by $80m$ in $2s$. The distance of upper point $A$ from the starting point is _____$m$. Use $(g=10m{s}^{-2})$

A stationary particle breaks into two parts of masses $m_A$ and $m_B$ which move with velocities $v_A$ and $v_B$ respectively. The ratio of their kinetic energies $\left(K_B: K_A\right)$ is :

Four identical particles of mass $m$ are kept at the four corners of a square. If the gravitational force exerted on one of the masses by the other masses is $(\frac{2\sqrt{2}+1}{32})\frac{G{m}^{2}}{{L}^{2}}$, the length of the sides of the square is

If a rubber ball falls from a height $h$ and rebounds upto the height of $h / 2$. The percentage loss of total energy of the initial system as well as velocity ball before it strikes the ground, respectively, are :

A coin is placed on a disc. The coefficient of friction between the coin and the disc is $\mu$. If the distance of the coin from the center of the disc is $r$, the maximum angular velocity which can be given to the disc, so that the coin does not slip away, is :

A wooden block of mass $5 \mathrm{~kg}$ rests on a soft horizontal floor. When an iron cylinder of mass $25 \mathrm{~kg}$ is placed on the top of the block, the floor yields and the block and the cylinder together go down with an acceleration of $0.1 \mathrm{~ms}^{-2}$. The action force of the system on the floor is equal to:

A sphere of relative density $\sigma$ and diameter $D$ has concentric cavity of diameter $d$. The ratio of $\frac{D}{d}$, if it just floats on water in a tank is :

The identical spheres each of mass $2M$ are placed at the corners of a right angled triangle with mutually perpendicular sides equal to $4m$ each. Taking point of intersection of these two sides as origin, the magnitude of position vector of the centre of mass of the system is $\frac{4\sqrt{2}}{x}$, where the value of $x$ is ________.

Two cars are travelling towards each other at speed of $20 \mathrm{~m} \mathrm{~s}^{-1}$ each. When the cars are $300 \mathrm{~m}$ apart, both the drivers apply brakes and the cars retard at the rate of $2 \mathrm{~m} \mathrm{~s}^{-2}$. The distance between them when they come to rest is :

The resultant of two vectors $\vec{A}$ and $\vec{B}$ is perpendicular to $\vec{A}$ and its magnitude is half that of $\vec{B}$. The angle between vectors $\vec{A}$ and $\vec{B}$ is ______ $\circ$.

The displacement and the increase in the velocity of a moving particle in the time interval of $t$ to $(t+1)s$ are $125m$ and $50m{s}^{-1}$, respectively. The distance travelled by the particle in $(t+2{)}^{\text{th }}s$ is ___________ $m$.

A spherical body of mass $100g$ is dropped from a height of $10m$ from the ground. After hitting the ground, the body rebounds to a height of $5m$. The impulse of force imparted by the ground to the body is given by: (given $g=9.8m{s}^{-2}$)

There are 100 divisions on the circular scale of a screw gauge of pitch $1 \mathrm{~mm}$. With no measuring quantity in between the jaws, the zero of the circular scale lies 5 divisions below the reference line. The diameter of a wire is then measured using this screw gauge. It is found that 4 linear scale divisions are clearly visible while 60 divisions on circular scale coincide with the reference line. The diameter of the wire is :

The de-Broglie wavelength associated with a particle of mass $m$ and energy $E$ is $h / \sqrt{2 m E}$. The dimensional formula for Planck's constant is :