Hi Raghav,

 Your problem has solved Please run given code.
 
 <apex:page controller="SearchRecords" showHeader="true" >
    <apex:form id="frm">
        <apex:actionFunction name="showcon" action="{!showContact}" reRender="frm" />
        <apex:pageblock >
            <apex:pageBlockSection title="Search Account Records" columns="1">
                Enter Name<apex:inputText value="{!getstring}" id="theTextInput"/>
            </apex:pageBlockSection>
            <apex:commandButton action="{!searchRecords}" value="Search" id="theSearch" reRender="frm"/>
            <apex:pageBlockSection title="Account Detail">
                <apex:pageBlocktable value="{!accountlist}" var="acc">
                    <apex:column >
                        <input type="radio" name="group1"/ >
                        <apex:actionSupport event="onclick" action="{!showContact}" ReRender="conpgblk">
                            <apex:param assignTo="{!accId}" name="accname" value="{!acc.id}"/>
                        </apex:actionSupport>
                    
                    </apex:column>
                    <apex:column value="{!acc.name}" headerValue="Account Name"/>
                    <apex:column value="{!acc.Phone}" headerValue="Phone"/>
                </apex:pageBlocktable>
            </apex:pageBlockSection>
            <apex:pageBlockSection title="Related Contact" id="conpgblk">
                <apex:pageBlockTable value="{!Contactlist}" var="con">
                    <apex:column value="{!con.LastName}" headerValue="Contact Name"/>
                    <apex:column value="{!con.Phone}" headerValue="Phone"/>
                    <apex:column value="{!con.Email}" headerValue="Email"/>
                    
                </apex:pageBlockTable>
            </apex:pageBlockSection>
        </apex:pageblock>
    </apex:form>
</apex:page>



public class SearchRecords {
    public String accId{get;set;}
    public string getstring{get;set;}
    public List<Account> accountlist {get;set;}
    public list<Contact> Contactlist{get;set;}
    public void searchRecords(){
        accountlist= new list<Account>();
        if(getstring!=null){
            accountlist= Database.query('select id,Name,Phone from Account where Name like \'%'+getstring+'%\'');
        }
    } 
    public PageReference showContact(){
        System.debug('AccId-->'+accId);
        Contactlist=[select Id,LastName,Email,Phone from contact where AccountId =:accId];  
        return null;
    }
}

Please mark it as best answer if you find it helpful.

Thank You
Ajay Dubedi