Physics

If the projection of $2\widehat{i}+4\widehat{j}-2\widehat{k}on\widehat{i}+2\widehat{j}+\alpha \widehat{k}$ $\stackrel{}{}\stackrel{}{}\stackrel{}{}\stackrel{}{}\stackrel{}{}\stackrel{}{}$ is zero. Then, the value of will be________.

A force on an object of mass 100g is $\left(10\widehat{i}+5\widehat{j}\right)N.$ The position of that object at t = 2s is $\left(a\widehat{i}+b\widehat{j}\right)m$ after starting from rest. The value of $\frac{a}{b}$ will be

The current in a coil of self inductance 2.0 H is increasing according to I = 2sin(t²)A. The amount of energy spent during the period when current changes from 0 to 2 A is…………J.

The total current supplied to the circuit is shown in figure by the 5 V battery is…………….A.

A resistor develops 300 J of thermal energy in 15s, when a current of 2 A is passed through it. If the current increases to 3 A, the energy developed in 10s is…………….J.

The equivalent capacitance between points A and B in below shown figure will be…………. $\mu F.$  

The first overtone frequency of an open organ pipe is equal to the fundamental frequency of a closed organ pipe. If the length of the closed organ pipe is 20cm. The length of the open organ pipe is……….cm.

A steam engine intakes 50g of steam at $100°C$  per minute and cools it down to $20°C.$  If latent heat of vaporization of steam is 540 cal g^-1, then the heat rejected by the steam engine per minute is………….* 10³ cal.

(Given : specific heat capacity of water : 1 cal g^{-1 0}C^-1)

The velocity of upper layer of water in a river is 36kmh^-1. Shearing stress between horizontal layers of water is 10^-3 Nm^-2. Depth of the river is…….m. (Co-efficient of viscosity of water is 10^-2 Pa.s)

A 0.5kg block moving at a speed of 12ms^-1 compresses a spring through a distance 30cm when its speed is halved. The spring constant of the spring will be…………Nm^-1.