Mechanics PYQ — Page 15

A body of mass $M$ thrown horizontally with velocity $v$ from the top of the tower of height $H$ touches the ground at a distance of $100 \mathrm{~m}$ from the foot of the tower. A body of mass $2 \mathrm{M}$ thrown at a velocity $\frac{v}{2}$ from the top of the tower of height $4 \mathrm{H}$ will touch the ground at a distance of _____$\mathrm{m}$.

The angle between vector $\vec{Q}$ and the resultant of $(2 \vec{Q}+2 \vec{P})$ and $(2 \vec{Q}-2 \vec{P})$ is :

A block of mass $1\mathrm{kg}$ is pushed up a surface inclined to horizontal at an angle of $60^{\circ}$ by a force of $10N$ parallel to the inclined surface as shown in figure. When the block is pushed up by $10m$ along inclined surface, the work done against frictional force is : $[g=10m{s}^{-2}]$ 

If $\mathrm{G}$ be the gravitational constant and $\mathrm{u}$ be the energy density then which of the following quantity have the dimensions as that of the $\sqrt{\mathrm{uG}}$ :

Two satellite $A$ and $B$ go round a planet in circular orbits having radii $4 R$ and $R$ respectively. If the speed of $\mathrm{A}$ is $3 v$, the speed of $\mathrm{B}$ will be :

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 $g=10m{s}^{-2}$) 

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 $(g=10m{s}^{-2})$

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 $g=9.8m{s}^{-2}$)

Given below are two statements : Statement (I) : Viscosity of gases is greater than that of liquids. Statement (II) : Surface tension of a liquid decreases due to the presence of insoluble impurities. In the light of the above statements, choose the most appropriate answer from the options given below :

Three blocks $M_1, M_2, M_3$ having masses $4 \mathrm{~kg}, 6 \mathrm{~kg}$ and $10 \mathrm{~kg}$ respectively are hanging from a smooth pully using rope 1,2 and 3 as shown in figure. The tension in the rope $1, T_1$ when they are moving upward with acceleration of $2 \mathrm{~ms}^{-2}$ is _____$\mathrm{N}\left(\right.$ if $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$ ). 

Given below are two statements : Statement I : When a capillary tube is dipped into a liquid, the liquid neither rises nor falls in the capillary. The contact angle may be $0^{\circ}$. Statement II : The contact angle between a solid and a liquid is a property of the material of the solid and liquid as well. In the light of the above statement, choose the correct answer from the options given below.

A thin circular disc of mass $M$ and radius $R$ is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with angular velocity $\omega$. If another disc of same dimensions but of mass $\mathrm{M} / 2$ is placed gently on the first disc co-axially, then the new angular velocity of the system is :

In an expression $a \times 10^{\mathrm{b}}$;

The relation between time ‘$t$’ and distance ‘$x$’ is $t=\alpha {x}^{2}+\beta x$, where $\alpha$ and $\beta$ are constants. The relation between acceleration $(a)$ and velocity $(v)$ is:

A plane is in level flight at constant speed and each of its two wings has an area of $40{m}^{2}.$ If the speed of the air is $180\mathrm{km}{h}^{-1}$ over the lower wing surface and $252\mathrm{km}{h}^{-1}$ over the upper wing surface, the mass of the plane is ________$\mathrm{kg}.$ (Take air density to be $1\mathrm{kg}{m}^{–3}$ and $g=10m{s}^{–2}$)

Position of an ant ( $S$ in metres) moving in $Y-Z$ plane is given by $S=2{t}^{2}\hat{j}+5\hat{k}$ (where $t$ is in second). The magnitude and direction of velocity of the ant at $t=1s$ will be :

A uniform thin metal plate of mass $10 \mathrm{~kg}$ with dimensions is shown. The ratio of $\mathrm{x}$ and $\mathrm{y}$ coordinates of center of mass of plate in $\frac{n}{9}$. The value of $n$ is ________ 

Each of three blocks $P,Q$ and $R$ shown in figure has a mass of $3\mathrm{kg}$. Each of the wire $A$ and $B$ has cross-sectional area $0.005{\mathrm{cm}}^{2}$ and Young's modulus $2\times {10}^{11}N{m}^{-2}$. Neglecting friction, the longitudinal strain on wire $B$ is _____ $\times {10}^{-4}$. (Take $g=10m{s}^{-2}$) 

A big drop is formed by coalescing $1000$ small droplets of water. The surface energy will become :

If $\vec{a}$ and $\vec{b}$ makes an angle $\cos ^{-1}\left(\frac{5}{9}\right)$ with each other, then $|\vec{a}+\vec{b}|=\sqrt{2}|\vec{a}-\vec{b}|$ for $|\vec{a}|=n|\vec{b}|$ The integer value of $\mathrm{n}$ is ____

When kinetic energy of a body becomes 36 times of its original value, the percentage increase in the momentum of the body will be:

One main scale division of a vernier caliper is equal to $m$ units. If $\mathrm{n}^{\text {th }}$ division of main scale coincides with $(n+1)^{\text {th }}$ division of vernier scale, the least count of the vernier caliper is :

If the percentage errors in measuring the length and the diameter of a wire are $0.1%$ each. The percentage error in measuring its resistance will be: