A body of mass $m$ is suspended by two strings making angles $\theta_{1}$ and $\theta_{2}$ with the horizontal ceiling with tensions $\mathrm{T}_{1}$ and $\mathrm{T}_{2}$ simultaneously. $\mathrm{T}_{1}$ and $\mathrm{T}_{2}$ are related by $\mathrm{T}_{1}=\sqrt{3} \mathrm{~T}_{2}$. the angles $\theta_{1}$ and $\theta_{2}$ are
Current passing through a wire as function of time is given as $I(t)=0.02 \mathrm{t}+0.01 \mathrm{~A}$. The charge that will flow through the wire from $t=1 \mathrm{~s}$ to $\mathrm{t}=2 \mathrm{~s}$ is:
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: The kinetic energy needed to project a body of mass $m$ from earth surface to infinity is $\frac{1}{2} \mathrm{mgR}$, where R is the radius of earth. Reason R: The maximum potential energy of a body is zero when it is projected to infinity from earth surface.
The Boolean expression $\mathrm{Y}=\mathrm{A} \overline{\mathrm{B}} \mathrm{C}+\overline{\mathrm{AC}}$ can be realised with which of the following gate configurations.A. One 3-input AND gate, 3 NOT gates and one 2-input OR gate, One 2-input AND gate B. One 3-input AND gate, 1 NOT gate, One 2-input NOR gate and one 2-input OR gate C. 3-input OR gate, 3 NOT gates and one 2-input AND gate Choose the correct answer from the options given below:
Two simple pendulums having lengths $l_{1}$ and $l_{2}$ with negligible string mass undergo angular displacements $\theta_{1}$ and $\theta_{2}$, from their mean positions, respectively. If the angular accelerations of both pendulums are same, then which expression is correct?
Two infinite identical charged sheets and a charged spherical body of charge density ' $\rho$ ' are arranged as shown in figure. Then the correct relation between the electrical fields at $\mathrm{A}, \mathrm{B}, \mathrm{C}$ and D points is:
An alternating current is represented by the equation, $\mathrm{i}=100 \sqrt{2} \sin (100 \pi \mathrm{t})$ ampere. The RMS value of current and the frequency of the given alternating current are
Consider the sound wave travelling in ideal gases of $\mathrm{He}, \mathrm{CH}_{4}$, and $\mathrm{CO}_{2}$. All the gases have the same ratio $\frac{\mathrm{P}}{\rho}$, where P is the pressure and $\rho$ is the density. The ratio of the speed of sound through the gases $\mathrm{v}_{\mathrm{He}}: \mathrm{v}_{\mathrm{CH}_{4}}: \mathrm{v}_{\mathrm{CO}_{2}}$ is given by
In an electromagnetic system, the quantity representing the ratio of electric flux and magnetic flux has dimension of $\mathrm{M}^{\mathrm{B}} \mathrm{L}^{\mathrm{O}} \mathrm{T}^{\mathrm{B}} \mathrm{A}^{\mathrm{S}}$, where value of 'Q' and 'R' are
When an object is placed 40 cm away from a spherical mirror an image of magnification $\frac{1}{2}$ is produced. To obtain an image with magnification of $\frac{1}{3}$, the object is to be moved:
Two liquids A and B have $\theta_{\mathrm{A}}$ and $\theta_{\mathrm{B}}$ as contact angles in a capillary tube. If $K=\cos \theta_{\mathrm{A}} / \cos \theta_{\mathrm{B}}$, then identify the correct statement:
Which of the following are correct expression for torque acting on a body? A. $\ddot{\tau}=\ddot{\mathrm{r}} \times \ddot{\mathrm{L}}$ B. $\ddot{\tau}=\frac{\mathrm{d}}{\mathrm{dt}}(\ddot{\mathrm{r}} \times \ddot{\mathrm{p}})$ C. $\ddot{\tau}=\ddot{\mathrm{r}} \times \frac{\mathrm{d} \dot{\mathrm{p}}}{\mathrm{dt}}$ D. $\ddot{\tau}=\mathrm{I} \dot{\alpha}$ E. $\ddot{\tau}=\ddot{\mathrm{r}} \times \ddot{\mathrm{F}}$ ( $\ddot{r}=$ position vector; $\dot{\mathrm{p}}=$ linear momentum; $\ddot{\mathrm{L}}=$ angular momentum; $\ddot{\alpha}=$ angular acceleration; $\mathrm{I}=$ moment of inertia; $\ddot{\mathrm{F}}=$ force; $\mathrm{t}=$ time $)$ Choose the correct answer from the options given below:
Consider two blocks A and B of masses \( m_1 = 10 \) kg and \( m_2 = 5 \) kg that are placed on a frictionless table. The block A moves with a constant speed \( v = 3 \) m/s towards the block B kept at rest. A spring with spring constant \( k = 3000 \) N/m is attached with the block B as shown in the figure. After the collision, suppose that the blocks A and B, along with the spring in constant compression state, move together, then the compression in the spring is, (Neglect the mass of the spring)
