Mechanics PYQ — Page 14

Given below are two statements: Statement I: The hot water flows faster than cold water Statement II: Soap water has higher surface tension as compared to fresh water. In the light above statements, choose the correct answer from the options given below

A massless spring gets elongated by amount $x_1$ under a tension of 5 N . Its elongation is $x_2$ under the tension of 7 N . For the elongation of $\left(5 x_1-2 x_2\right)$, the tension in the spring will be,

Two iron solid discs of negligible thickness have radii $R_1$ and $R_2$ and moment of intertia $I_1$ and $I_2$, respectively. For $R_2=2 R_1$, the ratio of $I_1$ and $I_2$ would be $1 / x$, where $\mathrm{x}=$ ________ -

A force of 49 N acts tangentially at the highest point of a sphere (solid) of mass 20 kg , kept on a rough horizontal plane. If the sphere rolls without slipping, then the acceleration of the center of the sphere is 

The fractional compression \(\left(\frac{\Delta \mathrm{V}}{\mathrm{V}}\right)\) of water at the depth of 2.5 km below the sea level is ______ \(\%\). Given, the Bulk modulus of water \(=2 \times 10^9 \mathrm{~N} \mathrm{~m}^{-2}\), density of water \(=10^3\) \(\mathrm{kg} \mathrm{m}^{-3}\), acceleration due to gravity \(=\mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2}\).

An object of mass 1000 g experiences a time dependent force $\vec{F}=\left(2 t \hat{i}+3 t^2 \hat{j}\right) N$. The power generated by the force at time $t$ is :

In an electromagnetic system, the quantity representing the ratio of electric flux and magnetic flux has dimension of $\mathrm{M}^{\mathrm{P}} \mathrm{L}^{\mathrm{Q}} \mathrm{T}^{\mathrm{R}} \mathrm{A}^{\mathrm{S}}$, where value of ' Q ' and ' R ' are

A quantity Q is formulated as $\mathrm{X}^{-2} \mathrm{Y}^{+\frac{3}{2}} \mathrm{Z}^{-\frac{2}{5}} \cdot \mathrm{X}, \mathrm{Y}$ and Z are independent parameters which have fractional errors of $0.1,0.2$ and 0.5 , respectively in measurement. The maximum fractional error of Q is

 A block is simply released from the top of an inclined plane as shown in the figure above. The maximum compression in the spring when the block hits the spring is :

A solid circular disc of mass $50\mathrm{kg}$ rolls along a horizontal floor so that its center of mass has a speed of $0.4m{s}^{-1}$. The absolute value of work done on the disc to stop it is ______ $J$.

A stone of mass $900g$ is tied to a string and moved in a vertical circle of radius $1m$ making $10\mathrm{rpm}$. The tension in the string, when the stone is at the lowest point is (if ${\pi }^{2}=9.8$ and $g=9.8m{s}^{-2}$)

A train is moving with a speed of $12m{s}^{-1}$ on rails which are $1.5m$ apart. To negotiate a curve radius $400m$, the height by which the outer rail should be raised with respect to the inner rail is (Given, $g=$ $10m{s}^{-2}$):

 A hydraulic press containing water has two arms with diameters as mentioned in the figure. A force of $10 \mathrm{~N}$ is applied on the surface of water in the thinner arm. The force required to be applied on the surface of water in the thicker arm to maintain equilibrium of water is _____N.

Given below are two statements: one is labelled as Assertion(A) and the other is labelled as Reason (R). Assertion (A) : In Vernier calliper if positive zero error exists, then while taking measurements, the reading taken will be more than the actual reading. Reason (R) : The zero error in Vernier Calliper might have happened due to manufacturing defect or due to rough handling. In the light of the above statements, choose the correct answer from the options given below :

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 metal wire of uniform mass density having length $L$ and mass $M$ is bent to form a semicircular arc and a particle of mass $\mathrm{m}$ is placed at the centre of the arc. The gravitational force on the particle by the wire is :

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 _____. 

Consider a block and trolley system as shown in figure. If the coefficient of kinetic friction between the trolley and the surface is $0.04$, the acceleration of the system in $m{s}^{-2}$ is: (Consider that the string is massless and unstretchable and the pulley is also massless and frictionless) : 

The density and breaking stress of a wire are $6 \times 10^4 \mathrm{~kg} / \mathrm{m}^3$ and $1.2 \times 10^8 \mathrm{~N} / \mathrm{m}^2$ respectively. The wire is suspended from a rigid support on a planet where acceleration due to gravity is $\frac{1}{3}^{\text {rd }}$ of the value on the surface of earth. The maximum length of the wire with breaking is _____ m (take, $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$ ).

The resistance $R=\frac{V}{I}$, where $V=(200\pm 5)V$ and $I=(20\pm 0.2)A$, the percentage error in the measurement of $R$ is :

A big drop is formed by coalescing 1000 small droplets of water. The ratio of surface energy of 1000 droplets to that of energy of big drop is $\frac{10}{x}$. The value of $x$ is __________

Given below are two statements: Statement I : When speed of liquid is zero everywhere, pressure difference at any two points depends on equation $P_1-P_2=\rho g\left(h_2-h_1\right)$. Statement II : In ventury tube shown $2 \mathrm{gh}=v_1^2-v_2^2$  In the light of the above statements, choose the most appropriate answer from the options given below.

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 $\sqrt{\mathrm{uG}}$ :

A physical quantity $Q$ is found to depend on quantities $a,b,c$ by the relation $Q=\frac{{a}^{4}{b}^{3}}{{c}^{2}}$. The percentage error in $a,b$ and $c$ are $3%,4%$ and $5%$ respectively. Then, the percentage error in $Q$ is: