Mechanics PYQ — Page 7

The energy required to break one bond in DNA is ${10}^{–20}J$. This value in $\mathrm{eV}$ is nearly

Time intervals measured by a clock give the following readings: $1.25s,1.24s,1.27s,1.21s$ and $1.28s$. What is the percentage relative error of the observations?

A body weighs $72N$ on the surface of the earth. What is the gravitational force on it, at a height equal to half the radius of the earth?

Two particles of mass $5 \mathrm{kg}$ and $10 \mathrm{kg}$ respectively are attached to the two ends of a rigid rod of length $1 m$ with negligible mass. The centre of mass of the system from the $5 \mathrm{kg}$ particle is nearly at a distance of:

The speed of a swimmer in still water is $20 m{s}^{-1}.$ The speed of river water is $10 m{s}^{-1}$ and is flowing due east. If he is standing on the south bank and wishes to cross the river along the shortest path, the angle at which he should make his strokes with respect to the north is given by

A force $F=20+10y$ acts on a particle in $y$-direction where $F$ is in Newton and $y$ is in meter. Work done by this force to move the particle from $y=0$ to $y=1 m$ is

When a block of mass $M$ is suspended by a long wire of length $L$, the length of the wire becomes $(L+l).$ The elastic potential energy stored in the extended wire is

A particle moving with velocity $\vec{V}$ is acted by three forces shown by the vector triangle $PQR$. The velocity of the particle will 

A small hole of area cross-section $2 m{m}^{2}$ is present near the bottom of a fully filled open tank of height $2 m.$ Taking $g=10 m{s}^{-2}$, the rate of flow of water through the open hole would be nearly

In an experiment, the percentage of error occurred in the measurement of physical quantities $A,B,C$ and $D$ are 1%, 2%, 3% and 4%, respectively. Then the maximum percentage of error in the measurement $X$, where $X=\frac{{A}^{2}{B}^{\frac{1}{2}}}{{C}^{\frac{1}{3}}{D}^{3}}$ will be

An object of mass $500 \mathrm{~g}$, initially at rest acted upon by a variable force whose $\mathrm{X}$ component varies with $\mathrm{X}$ in the manner shown. The velocities of the object a point $X=8 \mathrm{~m}$ and $X=12 \mathrm{~m}$, would be the respective values of (nearly) 

A body of mass $m$ is kept on a rough horizontal surface (coefficient of friction $=\mu$ ). Horizontal force is applied on the body, but it does not move. The resultant of normal reaction and the frictional force acting on the object is given $\mathrm{F}$, where $\mathrm{F}$ is

A particle of mass $5 \mathrm{~m}$ at rest suddenly breaks on its own into three fragments. Two fragments of mass m each move along mutually perpendicular direction with each speed v. The energy released during the process is

The time period of a geo-stationary satellite is $24 \mathrm{~h}$, at a height $6 R_E-R_E$ is the radius of earth) from surface of earth. The time period of another satellite whose height is $2.5 \mathrm{R}_{\mathrm{E}}$ from surface will be

The stress-strain curves are drawn for two different materials $\mathrm{X}$ and $\mathrm{Y}$. It is observed that the ultimate strength point and the fracture point are close to each other for material X but are far apart for material Y. We can say that materials $\mathrm{X}$ and $\mathrm{Y}$ are likely to be (respectively)

Two particles $A$ and $B$ are moving in uniform circular motion in concentric circles of radii ${r}_{A}$ and ${r}_{B}$ with speed ${v}_{A}$ and ${v}_{B}$, respectively. Their time period of rotation is the same. The ratio of angular speed of $A$ to that of $B$ will be,

A block of mass $10 kg$ is in contact against the inner wall of a hollow cylindrical drum of radius$1m$. The coefficient of friction between the block and the inner wall of the cylinder is $0.1$. The minimum angular velocity needed for the cylinder to keep the block stationary when the cylinder is vertical and rotating about its axis will be $(g=10 m{s}^{-2})$,

In a u-tube as shown in a figure, water and oil are in the left side and right side of the tube respectively. The heights from the bottom for water and oil columns are $15 \mathrm{~cm}$ and $20 \mathrm{~cm}$ respectively. The density of the oil is $\left[\right.$ take $\left.\rho_{\text {water }}=1000 \mathrm{~kg} / \mathrm{m}^3\right]$ 

The main scale of a vernier calliper has $\mathrm{n}$ divisions/cm. n divisions of the vernier scale coincide with $(n-1)$ divisions of main scale. The least count of the vernier callipers is

Two small spherical metal balls, having equal masses, are made from materials of densities $\rho_1$ and $\rho_2\left(\rho_1=8 \rho_2\right)$ and have radii of $1 \mathrm{~mm}$ and $2 \mathrm{~mm}$, respectively. They are made to fall vertically (from rest) in viscous medium whose coefficient of viscosity equals $\eta$ and whose density is $0.1 \rho_2$. The ratio of their terminal velocities would be

A particle starting from rest, moves in a circle of radius ' $r$ '. It attains a velocity of $\mathrm{v}_0 \mathrm{~m} / \mathrm{s}$ in the $\mathrm{n}^{\text {th }}$ round. Its angular acceleration will be

A person travelling in a straight line moves with a constant velocity $\mathrm{v}_1$ for certain distance ' $\mathrm{x}$ ' and with a constant velocity $\mathrm{v}_2$ for next equal distance. The average velocity $v$ is given by the relation

Two bullets are fired horizontally and simultaneously towards each other from roof tops of two buildings $100 \mathrm{~m}$ apart and of same height of $200 \mathrm{~m}$ with the same velocity of $25 \mathrm{~m} / \mathrm{s}$. When and where will the two bullets collides. $\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\right)$

A person standing on the floor of an elevator drops a coin. The coin reaches the floor in time $t_1$ if the elevator is at rest and in time $t_2$ if the elevator is moving uniformly. The which of the following option is correct?