Mechanics PYQ — Page 23

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 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 $\pi=3.14$ ) :

A circular table is rotating with an angular velocity of $\omega \mathrm{rad} / \mathrm{s}$ about its axis (see figure). There is a smooth groove along a radial direction on the table. A steel ball is gently placed at a distance of $1 \mathrm{~m}$ on the groove. All the surfaces are smooth. If the radius of the table is $3 \mathrm{~m}$, the radial velocity of the ball w.r.t. the table at the time ball leaves the table is $x \sqrt{2} \omega \mathrm{m} / \mathrm{s}$, where the value of $x$ is _____. 

A circular disc reaches from top to bottom of an inclined plane of length $l$. When it slips down the plane, if takes $t \mathrm{~s}$. When it rolls down the plane then it takes $\left(\frac{\alpha}{2}\right)^{1 / 2} t \mathrm{~s}$, where $\alpha$ is _________

A car of $800 \mathrm{~kg}$ is taking turn on a banked road of radius $300 \mathrm{~m}$ and angle of banking $30^{\circ}$. If coefficient of static friction is 0.2 then the maximum speed with which car can negotiate the turn safely: $\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2, \sqrt{3}=1.73\right)$

A bus moving along a straight highway with speed of $72 \mathrm{~km} / \mathrm{h}$ is brought to halt within $4 s$ after applying the brakes. The distance travelled by the bus during this time (Assume the retardation is uniform) is _____m.

A bullet of mass $50 \mathrm{~g}$ is fired with a speed $100 \mathrm{~m} / \mathrm{s}$ on a plywood and emerges with $40 \mathrm{~m} / \mathrm{s}$. The percentage loss of kinetic energy is :

A bullet is fired into a fixed target looses one third of its velocity after travelling $4\mathrm{cm}$. It penetrates further $D\times {10}^{-3}m$ before coming to rest. The value of $D$ is :

A $2 \mathrm{~kg}$ brick begins to slide over a surface which is inclined at an angle of $45^{\circ}$ with respect to horizontal axis. The co-efficient of static friction between their surfaces is:

A body travels $102.5 \mathrm{~m}$ in $\mathrm{n}^{\text {th }}$ second and $115.0 \mathrm{~m}$ in $(\mathrm{n}+2)^{\text {th }}$ second. The acceleration is :

A body starts moving from rest with constant acceleration covers displacement ${S}_{1}$ in first $(p-1)$ seconds and ${S}_{2}$ in first $p$ seconds. The displacement ${S}_{1}+{S}_{2}$ will be made in time :

A body starts falling freely from height $H$ hits an inclined plane in its path at height $h$. As a result of this perfectly elastic impact, the direction of the velocity of the body becomes horizontal. The value of $\frac{H}{h}$ for which the body will take the maximum time to reach the ground is _____.

A body projected vertically upwards with a certain speed from the top of a tower reaches the ground in $t_1$. If it is projected vertically downwards from the same point with the same speed, it reaches the ground in $t_2$. Time required to reach the ground, if it is dropped from the top of the tower, is :

A $90 \mathrm{~kg}$ body placed at $2 \mathrm{R}$ distance from surface of earth experiences gravitational pull of : $\text { ( } \mathrm{R}=\text { Radius of earth, } \mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2} \text { ) }$

A body of weight $200 \mathrm{~N}$ is suspended from a tree branch through a chain of mass $10 \mathrm{~kg}$. The branch pulls the chain by a force equal to (if $g=10 \mathrm{~m} / \mathrm{s}^2$ ) :

A body of $m \mathrm{~kg}$ slides from rest along the curve of vertical circle from point $A$ to $B$ in friction less path. The velocity of the body at $B$ is:  $\text { (given, } R=14 \mathrm{~m}, g=10 \mathrm{~m} / \mathrm{s}^2 \text { and } \sqrt{2}=1.4 \text { ) }$

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 _____$\mathrm{m}$.

A body of mass $5\mathrm{kg}$ moving with a uniform speed $3\sqrt{2}m{s}^{-1}$ in $X-Y$ plane along the line $y=x+4$. The angular momentum of the particle about the origin will be _______$\mathrm{kg}{m}^{2}{s}^{-1}$.

A body of mass $m$ is projected with a speed $u$ making an angle of ${45}^{o}$ with the ground. The angular momentum of the body about the point of projection, at the highest point is expressed as $\frac{\sqrt{2}m{u}^{3}}{Xg}$. The value of $X$ is_______.

A body of mass $1000\mathrm{kg}$ is moving horizontally with a velocity $6m{s}^{-1}$. If $200\mathrm{kg}$ extra mass is added, the final velocity (in $m{s}^{-1}$) is:

A body of mass $50 \mathrm{~kg}$ is lifted to a height of $20 \mathrm{~m}$ from the ground in the two different ways as shown in the figures. The ratio of work done against the gravity in both the respective cases, will be : 

A body of mass $4\mathrm{kg}$ experiences two forces ${\vec{F}}_{1}=5\hat{i}+8\hat{j}+7\hat{k}$ and ${\vec{F}}_{2}=3\hat{i}-4\hat{j}-3\hat{k.}$ The acceleration acting on the body is:

A body of mass $2\mathrm{kg}$ begins to move under the action of a time dependent force given by $\vec{F}=(6t\hat{i}+6{t}^{2}\hat{j})N$. The power developed by the force at the time $t$ is given by:

A body moves on a frictionless plane starting from rest. If $S_n$ is distance moved between $t=n-1$ and $\mathrm{t}=\mathrm{n}$ and $\mathrm{S}_{\mathrm{n}-1}$ is distance moved between $\mathrm{t}=\mathrm{n}-2$ and $\mathrm{t}=\mathrm{n}-1$, then the ratio $\frac{\mathrm{S}_{\mathrm{n}-1}}{\mathrm{~S}_{\mathrm{n}}}$ is $\left(1-\frac{2}{x}\right)$ for $\mathrm{n}=10$. The value of $x$ is ______.