The velocity ($v$) – time ($t$) plot of the motion of a body is shown below:
The acceleration ($a$) – time ($t$) graph that best suits this motion is:
Trapezoidal $v$–$t$ → positive constant $a$, then $a = 0$, then negative constant $a$.
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The velocity ($v$) – time ($t$) plot of the motion of a body is shown below:
The acceleration ($a$) – time ($t$) graph that best suits this motion is:
Trapezoidal $v$–$t$ → positive constant $a$, then $a = 0$, then negative constant $a$.
If the mass of the bob in a simple pendulum is increased to thrice its original mass and its length is made half its original length, then the new time period of oscillation is $\dfrac{x}{2}$ times its original time period. Then the value of $x$ is:
$T \propto \sqrt L$, mass-independent. $T_\text{new}/T_\text{old} = \sqrt{1/2} = x/2 \Rightarrow x = \sqrt 2$.
A metallic bar of Young's modulus, $0.5\times 10^{11}\ \text{N m}^{-2}$ and coefficient of linear thermal expansion $10^{-5}\ {}^\circ\text{C}^{-1}$, length 1 m and area of cross-section $10^{-3}\ \text{m}^2$ is heated from $0\,{}^\circ\text{C}$ to $100\,{}^\circ\text{C}$ without expansion or bending. The compressive force developed in it is:
$F = YA\alpha\Delta T = 0.5\times 10^{11} \cdot 10^{-3} \cdot 10^{-5} \cdot 100 = 5\times 10^4 = 50\times 10^3$ N.
A sheet is placed on a horizontal surface in front of a strong magnetic pole. A force is needed to:
A. hold the sheet there if it is magnetic.
B. hold the sheet there if it is non-magnetic.
C. move the sheet away from the pole with uniform velocity if it is conducting.
D. move the sheet away from the pole with uniform velocity if it is both, non-conducting and non-polar.
Choose the correct statement(s) from the options given below:
Magnetic sheet attracted (A needs holding force); conducting sheet feels eddy-current drag (C needs pushing force).
The property which is not of an electromagnetic wave travelling in free space is that:
EM waves are produced by accelerating charges, not uniformly moving ones.
A parallel plate capacitor is charged by connecting it to a battery through a resistor. If I is the current in the circuit, then in the gap between the plates:
In the gap $I_\text{disp} = \epsilon_0\,d\Phi_E/dt$ equals the conduction current $I$ and points the same way.
An iron bar of length L has magnetic moment M. It is bent at the middle of its length such that the two arms make an angle $60^\circ$ with each other. The magnetic moment of this new magnet is:
Each half $= M/2$. With $60^\circ$ between arms, moment vectors are $120^\circ$ apart. Resultant $= 2(M/2)\cos 60^\circ = M/2$.
The minimum energy required to launch a satellite of mass $m$ from the surface of earth of mass $M$ and radius $R$ in a circular orbit at an altitude of $2R$ from the surface of the earth is:
$E_\text{orbit}(3R) - E_\text{surface} = -GMm/(2\cdot 3R) - (-GMm/R) = 5GMm/(6R)$.
The following graph represents the T-V curves of an ideal gas (where T is the temperature and V the volume) at three pressures $P_1$, $P_2$ and $P_3$ compared with those of Charles's law represented as dotted lines.
Then the correct relation is:
Slope of $T$-$V$ at fixed $P$ $\propto P/nR$ → steeper curve = higher pressure → $P_1 > P_2 > P_3$.
A force defined by $F = \alpha t^2 + \beta t$ acts on a particle at a given time $t$. The factor which is dimensionless, if $\alpha$ and $\beta$ are constants, is:
$[\alpha] = MLT^{-4}$, $[\beta] = MLT^{-3}$, so $\alpha t/\beta$ is dimensionless.
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