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The horizontal range and the maximum height of a projectile are equal. The angle of projection of the projectile is:
Two racing cars of masses $m_1$ and $m_2$ are moving in circles of radii $r_1$ and $r_2$ respectively. Their speeds are such that each makes a complete circle in the same duration of time $t$. The ratio of the angular speed of the first to the second car is:
Match List-I with List-II. **List-I (Material)** (A) Diamagnetic (B) Ferromagnetic (C) Paramagnetic (D) Non-magnetic **List-II (Susceptibility $\chi$)** (I) $\chi = 0$ (II) $0 > \chi \ge -1$ (III) $\chi \gg 1$ (IV) $0 < \chi < \epsilon$ (a small positive number) Choose the correct answer from the options given below:
A wire of length $L$, area of cross section $A$ is hanging from a fixed support. The length of the wire changes to $L_1$ when mass $M$ is suspended from its free end. The expression for Young's modulus is:
Two wires are made of the same material and have the same volume. The first wire has a cross-sectional area $A$ and the second wire has a cross-sectional area $3A$. If the length of the first wire is increased by $\Delta l$ on applying a force $F$, how much force is needed to stretch the second wire by the same amount?
A 150 m long train is moving to north at a speed of 10 m/s. A parrot flying towards south with a speed of 5 m/s crosses the train. The time taken by the parrot to cross the train would be:
The angular speed of the seconds needle in a mechanical watch is:
In a uniform magnetic field of $0.049 \text{ T}$, a magnetic needle performs $20$ complete oscillations in $5$ seconds as shown. The moment of inertia of the needle is $9.8 \times 10^{-6} \text{ kg m}^2$. If the magnitude of magnetic moment of the needle is $x \times 10^{-5} \text{ Am}^2$, then the value of '$x$' is:
A stone tied to the end of a string of 1 m long is whirled in a horizontal circle with a constant speed. If the stone makes 22 revolutions in 44 s, what is the magnitude and direction of acceleration of the stone?
Let a wire be suspended from the ceiling (rigid support) and stretched by a weight $W$ attached at its free end. The longitudinal stress at any point of the cross-sectional area $A$ of the wire is:
A projectile is fired at an angle of $45^{\circ}$ with the horizontal. The elevation angle $\alpha$ of the projectile at its highest point as seen from the point of projection is:
At point A on the earth's surface, the angle of dip is, $\delta=+25^\circ$. At a point B on the earth's surface, the angle of dip is, $\delta=-25^\circ$. We can interpret that:
A wire of length $L$ and radius $r$ ($r \ll L$) is kept floating on the surface of a liquid of density $\rho$. The maximum radius of the wire for which it may not sink is: (the surface tension of liquid is $T$)
The magnitude and direction of the current in the following circuit is
A missile is fired for a maximum range with an initial velocity of $20 \text{ m/s}$. If $g=10 \text{ m/s}^2$, then the range of the missile will be:
The following four wires are made of the same material. Which of them will have the largest extension when the same tension is applied?
A particle has initial velocity $(3\hat{i}+4\hat{j})$ and has acceleration $(0.4\hat{i}+0.3\hat{j})$. Its speed after $10 \text{ s}$ is:
What is the value of linear velocity if $\vec{\omega} = 3\hat{i} - 4\hat{j} + \hat{k}$ and $\vec{r} = 5\hat{i} - 6\hat{j} + 6\hat{k}$:
A ball is thrown upwards and it returns to the ground describing a parabolic path. Which of the following remains constant?
A ball is projected with velocity $v_0$ at an angle of elevation $30^{\circ}$. Mark the correct statement.