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What is the minimum velocity with which a body of mass $m$ must enter a vertical loop of radius $R$ so that it can complete the loop?
A body of mass $1 \text{ kg}$ begins to move under the action of a time-dependent force $\vec{F} = (2t\hat{i} + 3t^2\hat{j}) \text{ N}$, where $\hat{i}$ and $\hat{j}$ are unit vectors along the X and Y axes. What power will be developed by the force at time $t$?
Placentation, in which ovules develop on the inner wall of the ovary or in peripheral part, is:
A ball is thrown vertically downwards from a height of $20 \text{ m}$ with an initial velocity $v_0$. It collides with the ground, loses $50\%$ of its energy in a collision and rebounds to the same height. The initial velocity $v_0$ is: (Take $g = 10 \text{ m/s}^2$)
The factor that leads to Founder effect in a population is:
The animal coelacanth caught in South Africa is an example of vertebrate transition from:
On a frictionless surface, a block of mass $M$ moving at speed $v$ collides elastically with another block of same mass $M$ which is initially at rest. After collision the first block moves at an angle $\theta$ to its initial direction and has a speed $v/3$. The second block's speed after the collision is:
An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right angles to each other. The first part of mass $1 \text{ kg}$ moves with a speed of $12 \text{ m s}^{-1}$ and the second part of mass $2 \text{ kg}$ moves with $8 \text{ m s}^{-1}$ speed. If the third part flies off with $4 \text{ m s}^{-1}$ speed, then its mass is:
Which of the following muscular disorders is inherited?
Two cars moving in opposite directions approach each other with speed of $22 \text{ m/s}$ and $16.5 \text{ m/s}$ respectively. The driver of the first car blows a horn having a frequency $400 \text{ Hz}$. The frequency heard by the driver of the second car is [velocity of sound $340 \text{ m/s}$]
If we study the vibration of a pipe open at both ends, then the following statement is not true:
A wave travelling in the positive x-direction having maximum displacement along y-direction as $1 \text{ m}$, wavelength $2\pi \text{ m}$ and frequency of $1/\pi \text{ Hz}$ is represented by
Purines found both in DNA and RNA are
The equation of a simple harmonic wave is given by $y=3\sin\frac{\pi}{2}(50t-x)$ where $x$ and $y$ are in meters and $t$ is in seconds. The ratio of maximum particle velocity to the wave velocity is:
Two waves are represented by the equations $y_1=a\sin(\omega t+kx+0.57)\text{ m}$ and $y_2=a\cos(\omega t+kx)\text{ m}$, where $x$ is in metre and $t$ in second. The phase difference between them is:
A tuning fork of frequency $512 \text{ Hz}$ makes $4 \text{ beats/s}$ with the vibrating strings of a piano. The beat frequency decreases to $2 \text{ beats/s}$ when the tension in the piano strings is slightly increased. The frequency of the piano string before increasing the tension was:
A wave in a string has an amplitude of $2 \text{ cm}$. The wave travels in the +ve direction of x-axis with a speed of $128 \text{ ms}^{-1}$ and it is noted that $5$ complete waves fit in $4 \text{ m}$ length of the string. The equation describing the wave is:
What is the product formed in the below reaction? (Note: Reactant structure is missing) + $NaNO_2 + HCl \longrightarrow$ Product
A wave traveling in the +ve x-direction having maximum displacement along y-direction as $1 \text{ m}$, wavelength $2\pi \text{ m}$ and frequency of $1/\pi \text{ Hz}$, is represented by:
Each of the two strings of lengths $51.6 \text{ cm}$ and $49.1 \text{ cm}$ is tensioned separately by $20 \text{ N}$ of force. The mass per unit length of both strings is the same and equals $1 \text{ g/m}$. When both the strings vibrate simultaneously, the number of beats is: